U.S. patent application number 11/981428 was filed with the patent office on 2008-03-13 for automated data alignment based upon indirect device relationships.
This patent application is currently assigned to Square D Company. Invention is credited to Jon A. Bickel.
Application Number | 20080065712 11/981428 |
Document ID | / |
Family ID | 40541384 |
Filed Date | 2008-03-13 |
United States Patent
Application |
20080065712 |
Kind Code |
A1 |
Bickel; Jon A. |
March 13, 2008 |
Automated data alignment based upon indirect device
relationships
Abstract
A noisy data alignment algorithm for determining cycle count
offsets for noisy pairs of n monitoring devices. A direct cycle
count offset matrix is determined based upon the highest
correlation coefficients produced by correlating frequency
variation data from each device pair D.sub.ij. For each direct
cycle count offset M.sub.ij, indirect cycle count offsets are
calculated as a function of at least M.sub.k, where
k.noteq.i.noteq.j, to produce indirect cycle count offsets. The
statistical mode of these indirect offsets is compared with the
corresponding M.sub.ij in the matrix. When they differ, M.sub.ij in
the direct matrix is adjusted to be equal to the statistical mode.
All indirect cycle count offsets for all other unique device pairs,
M.sub.ij, are calculated to iterate to a single solution in which
all indirect cycle count offsets are equal to the corresponding
direct cycle count offset. An optional verification algorithm is
also provided.
Inventors: |
Bickel; Jon A.;
(Murfreesboro, TN) |
Correspondence
Address: |
SCHNEIDER ELECTRIC / SQUARE D COMPANY;LEGAL DEPT. - I.P. GROUP (NP)
1415 S. ROSELLE ROAD
PALATINE
IL
60067
US
|
Assignee: |
Square D Company
|
Family ID: |
40541384 |
Appl. No.: |
11/981428 |
Filed: |
October 31, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11174099 |
Jul 1, 2005 |
|
|
|
11981428 |
Oct 31, 2007 |
|
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Current U.S.
Class: |
708/422 |
Current CPC
Class: |
G01D 4/002 20130101;
Y04S 20/30 20130101; Y02B 90/20 20130101; H02J 13/0006
20130101 |
Class at
Publication: |
708/422 |
International
Class: |
G06F 17/15 20060101
G06F017/15 |
Claims
1. A method of automatically aligning data measured by a number, n,
of monitoring devices in a power monitoring system, comprising:
receiving from each of said monitoring devices respective signal
data representing at least frequency variations measured by
respective ones of said monitoring devices, said monitoring devices
including a reference monitoring device and a second monitoring
device; correlating said signal data from said reference monitoring
device with said signal data from said second monitoring device to
determine a reference cycle count, M.sub.i, associated with said
reference monitoring device corresponding to a maximum correlation
coefficient and a second cycle count, M.sub.j, associated with said
second monitoring device corresponding to said maximum correlation
coefficient; automatically calculating a direct cycle count offset,
M.sub.ij, as a function of a difference between said reference
cycle count, M.sub.i, and said second cycle count, M.sub.j, and
storing said direct cycle count offset in a direct cycle count
offset matrix; and automatically calculating an indirect cycle
count offset as a function of at least M.sub.k, where
k.noteq.i.noteq.j and 1.ltoreq.k.ltoreq.n, said M.sub.k being a
cycle count associated with a monitoring device of said n
monitoring devices other than said reference monitoring device and
other than said second monitoring device.
2. The method of claim 1, wherein said automatically calculating
said indirect cycle count offset is carried out with respect to at
least two other of said n monitoring devices except said reference
monitoring device and except said second monitoring device to
produce at least two indirect cycle count offsets including said
indirect cycle count offset.
3. The method of claim 2, further comprising determining which of
said at least 2 indirect cycle count offsets differs from said
direct cycle count offset.
4. The method of claim 2, further comprising: determining a
statistical mode from a set comprised of said at least 2 indirect
cycle count offsets to produce a mode value; and determining
whether the mode value differs from said direct cycle count
offset.
5. The method of claim 1, further comprising, responsive to said
direct cycle count offset differing from said indirect cycle count
offset, producing a modified direct cycle count offset equal to
said indirect cycle count offset.
6. The method of claim 5, further comprising storing an indication
that said signal data associated with said reference monitoring
device and said signal data associated with said second monitoring
device are aligned.
7. The method of claim 5, further comprising communicating said
modified direct cycle count offset to said reference monitoring
device or to said second monitoring device to cause said reference
monitoring device or said second monitoring device to adjust a
cycle counter in said reference monitoring device or in said second
monitoring device by a value corresponding to said modified direct
cycle count offset.
8. The method of claim 1, wherein said indirect cycle count offset
is a function of at least M.sub.ik-M.sub.jk.
9. The method of claim 1, wherein said indirect cycle count offset
is a function of at least M.sub.m, where m.noteq.i.noteq.j and
1.ltoreq.m.ltoreq.n, said M.sub.m being a cycle count associated
with a monitoring device of said n monitoring devices other than
said reference monitoring device and other than said second
monitoring device and other than said monitoring device associated
with M.sub.k.
10. The method of claim 1, further comprising determining a first
verification cycle count, M.sub.i', associated with said reference
monitoring device corresponding to a first correlation coefficient
that is less than said maximum correlation coefficient; determining
a second verification cycle count, M.sub.j', associated with said
second monitoring device corresponding to said first correlation
coefficient; automatically calculating a verification cycle count
offset, M.sub.ij', based upon the difference between said first
verification cycle count, M.sub.i', and said second verification
cycle count, M.sub.j', and storing said verification cycle count
offset; and responsive to said verification cycle count offset
equaling said indirect cycle count offset, storing an indication of
a level of confidence in said indirect cycle count offset based
upon said first correlation coefficient.
11. The method of claim 10, wherein said first correlation
coefficient is above a predetermined threshold below said maximum
correlation coefficient.
12. The method of claim 1, wherein said direct cycle count offset
matrix is an (n.times.n) skew-symmetric matrix.
13. The method of claim 1, wherein said frequency variations
represented by said first signal data are variations in fundamental
frequency or variations in harmonic frequency, wherein said
variations are associated with a voltage or a current.
14. The method of claim 1, wherein each of said n monitoring
devices includes a cycle counter, the method further comprising
communicating simultaneously a signal to said n monitoring devices
to reset their respective cycle counters.
15. A method of automatically aligning data measured by a number,
n, of monitoring devices in a power, monitoring system, comprising:
receiving from each of said monitoring devices respective signal
data, S.sub.n, representing at least frequency variations measured
by respective ones of said monitoring devices; for each of a
plurality of device pairs within a set comprising said n number of
monitoring devices, wherein each device pair is termed D.sub.ij,
where i.noteq.j, where 1.ltoreq.i.ltoreq.n, and where
1.ltoreq.j.ltoreq.n, correlating said signal data S.sub.i with said
signal data S.sub.j for each of said device pairs, D.sub.ij, to
determine respective cycle counts, M.sub.i and M.sub.j, associated
with D.sub.i and D.sub.j, respectively, said cycle counts
corresponding to a maximum correlation coefficient produced by said
correlating; for each of said device pairs, D.sub.ij, automatically
calculating a direct cycle count offset, M.sub.ij=M.sub.i-M.sub.j,
and storing said direct cycle count offset in a direct cycle count
offset matrix; for each of said direct cycle count offsets,
M.sub.ij, automatically calculating a plurality of indirect cycle
count offsets as a function of at least M.sub.k, said M.sub.k being
a cycle count associated with a monitoring device of said n
monitoring devices other than said reference monitoring device and
other than said second monitoring device, where
1.ltoreq.k.ltoreq.n, and k.noteq.i.noteq.j; storing said plurality
of indirect cycle count offsets for each M.sub.ij in an indirect
cycle count offset matrix; for each of said direct cycle count
offsets, M.sub.ij, in said direct cycle count offset matrix,
determining whether M.sub.ij is not equal to at least one of said
plurality of indirect cycle count offsets, and, responsive thereto,
storing an indication that M.sub.ij in said direct cycle count
offset matrix is equal to a value corresponding to said at least
one of said indirect cycle count offsets.
16. The method of claim 15, further comprising communicating an
indication of said value to D.sub.i or D.sub.j to cause D.sub.i or
D.sub.j to adjust a cycle counter by an amount corresponding to
said value.
17. The method of claim 15, further comprising communicating a
signal to each of said n monitoring devices to reset respective
cycle counters in each of said n monitoring devices at
substantially the same time.
18. The method of claim 15, further comprising: determining a
statistical mode from a set comprised of said indirect cycle count
offsets for M.sub.ij to produce a mode value; and determining
whether said mode value equals M.sub.ij in said direct cycle count
offset matrix.
19. The method of claim 15, wherein said correlating produces a
plurality of correlation coefficients including said maximum
correlation coefficient, the method further comprising: for said
devices D.sub.i and D.sub.j corresponding to said modified
M.sub.ij, determining a plurality of probable cycle count offsets
associated with a predetermined number of said plurality of
correlation coefficients that are less than said maximum
correlation coefficient; and responsive to one of said plurality of
said probable cycle count offsets equaling said modified M.sub.ij,
storing an indication of a level of confidence in said modified
M.sub.ij commensurate with how proximal a correlation coefficient
of said plurality of said correlation coefficients corresponding to
said one of said plurality of said probable cycle count offsets is
to said maximum correlation coefficient.
20. The method of claim 15, further comprising: receiving from at
least one of said monitoring devices second signal data
representing at least frequency variations measured by said at
least one of said monitoring devices; and adjusting a cycle count
associated with said at least one of said monitoring devices by
said value corresponding to said at least one of said indirect
cycle count offsets.
21. A method of automatically aligning data monitored by a number,
n, of monitoring devices, D, associated with a power monitoring
system, comprising: automatically correlating respective signal
data from a pair of said monitoring devices, D.sub.i and D.sub.j,
to determine a maximum correlation coefficient associated with
respective cycle counts for said pair of monitoring devices,
D.sub.ij, said respective signal data representing frequency
variations monitored by said D.sub.i and said D.sub.j,
respectively; determining a first cycle count offset, M.sub.ij, by
calculating a difference between said respective cycle counts;
determining a second cycle count offset from a function that
includes at least a cycle count associated with a monitoring device
of said monitoring devices other than D.sub.i or D.sub.j; and
storing an indication that said first cycle count offset is equal
to a value corresponding to said second cycle count offset.
22. The method of claim 21, further comprising communicating an
instruction to said D.sub.i or to said D.sub.j to adjust a cycle
counter, which stores said respective cycle counts, by an amount
corresponding to said value.
23. The method of claim 21, wherein said automatically correlating
includes determining whether said second cycle count offset equals
a cycle count offset associated with a correlation coefficient that
is less than said maximum correlation coefficient.
Description
RELATED APPLICATION
[0001] This application is related to co-pending U.S. application
Ser. No. 11/174,099, entitled "Automated Precision Alignment of
Data in a Utility Monitoring System," filed Jul. 1, 2005.
FIELD OF THE INVENTION
[0002] Aspects disclosed herein relate generally to utility
monitoring systems, and, in particular, to automated precision
alignment of data among monitoring devices.
BACKGROUND OF THE INVENTION
[0003] Since the introduction of electrical power distribution
systems in the late 19.sup.th century, there has been a need to
monitor their operational and electrical characteristics. The
ability to collect, analyze, and respond to information about the
electrical power system can improve safety, minimize equipment
loss, decrease scrap, and ultimately save time and money. To that
end, monitoring devices were developed to measure and report such
information. With the dawn of the electronics age, the quality and
quantity of data from monitoring devices was vastly improved, and
communications networks and software were developed to collect,
display and store information. Unfortunately, those responsible for
evaluating data from monitoring devices are now overwhelmed by
information from their monitoring systems. In the endeavor to
maximize the usefulness of a monitoring system, monitoring
equipment manufacturers are seeking methods of presenting
information in the most useful format.
[0004] Effectively monitoring today's electrical power distribution
systems is cumbersome, expensive, and inefficient. Electric power
monitoring systems are typically arranged in a hierarchy with
monitoring devices such as electrical meters installed at various
levels of the hierarchy (refer to FIG. 2). Monitoring devices
measure various characteristics of the electrical signal (e.g.,
voltage, current, waveform distortion, power, etc.) passing through
the conductors, and the data from each monitoring device is
analyzed by the user to evaluate potential performance or
quality-related issues. However, the components of today's
electrical monitoring systems (monitoring devices, software, etc.)
act independently of each other, requiring the user to be an expert
at configuring hardware, collecting and analyzing data, and
determining what data is vital or useful. There are two problems
here: the amount of data to be analyzed and the context of the
data. These are separate but related issues. It is possible to
automate the analysis of the data to address the amount of data.
But, in order to do this reliably, the data must be put into
context. The independence of data between each monitoring device
evaluating the electrical system essentially renders each
monitoring device oblivious of data from other monitoring devices
connected to the system being analyzed. Accordingly, the data
transmitted to the system computer from each monitoring device is
often misaligned in that data from each monitoring device on the
system does not arrive at the monitoring system's computer
simultaneously. There are two basic reasons for the temporal
misalignment of data between monitoring devices: communications
time delays and monitoring device timekeeping & event time
stamping. It is then up to the user to analyze and interpret this
independent data in order to optimize performance or evaluate
potential quality-related concerns on the electrical system.
[0005] Sophisticated processing capabilities in digital monitoring
devices allow large amounts of complex electrical data to be
derived and accumulated from a seemingly simple electrical signal.
Because of the data's complexity, quantity, and relative disjointed
relationship from one monitoring device to the next, manual
analysis of all the data is an enormous effort that often requires
experts to be hired to complete the task. This process is tedious,
complex, prone to error and oversight, and time-consuming. A
partial solution has been to use global positioning satellite (GPS)
systems to timestamp an event, but this approach requires that the
user purchase and install additional hardware and data lines to
link the monitoring devices together. And this solution still
requires the evaluation of large amounts of data because the system
is only temporally in context; not spatially in context.
Synchronizing data using GPS systems is also disadvantageous
because of time delays associated with other hardware in the
system. Loss of the signal from the GPS satellites renders this
approach nonfunctional. Furthermore, any alignment of data by a
GPS-based system can only be as accurate as the propagation delay
of the GPS signal, which means that the data still may not be
optimally aligned when a GPS system is used.
[0006] The addition of supplemental monitoring devices in the
electrical system does nothing more than generate more information
about the electrical system at the point where the meter is added
in the electrical system, increasing complexity without any
benefit. Any usefulness of the data is generally limited to the
locality of the monitoring device that was added, while even more
data is amassed.
[0007] The complexity of many electrical systems usually
necessitates an involved configuration process of monitoring
systems because each metered point in the electrical system has
different characteristics, which is why multiple monitoring devices
are installed in the first place. As a result of the enormous
volume of complex data accumulated from electrical monitoring
systems heretofore, a thorough analysis of the data is typically
not feasible due to limited resources, time, and/or experience.
[0008] Temporal alignment of the data is one important aspect to
understand and characterize the power system. Another important
aspect is having a thorough knowledge of the power monitoring
system's layout (or hierarchy). Power monitoring devices measure
the electrical system's operating parameters, but do not provide
information about how the parameters at different points on the
power monitoring system relate to each other. Knowing the hierarchy
of the power monitoring system puts the operating parameters of
multiple monitoring devices into context with each other.
[0009] To determine the layout of a power monitoring system, a user
must review electrical one-line drawings or physically perform an
inventory of the electrical system if one-line drawings are
unavailable. The user manually enters the spatial information into
the monitoring system software for analysis. When a new device or
monitored load is added or moved within the power monitoring
system, the user must manually update the monitoring system
software to reflect the new addition or change.
[0010] Data alignment and layout information are essential to
understanding and characterizing the power system. With these two
pieces of information, the data from each meter can be integrated
and put into context with every other meter in the power system.
Heretofore, the only techniques for passably integrating data were
complex, expensive, manually intensive, and time-consuming for the
user. These techniques also permit only limited integration of data
and require additional hardware (such as GPS hardware), data lines,
and supplemental monitoring device accessories.
[0011] What is needed, therefore, is an automated data integration
technique, including automatic precision alignment of data and
automatic hierarchical classification of system layout. The present
invention is directed to satisfying this and other needs.
SUMMARY OF THE INVENTION
[0012] Briefly, according to an embodiment of the present
invention, a method of aligning data measured by monitoring devices
coupled to a power monitoring system includes receiving reference
signal data from a reference monitoring device. The reference
signal data represents frequency variations measured by the
reference monitoring device for a predetermined number of cycles.
The method further includes receiving second signal data from a
second monitoring device that measures frequency variations for a
predetermined number of cycles. The method further includes
automatically aligning the reference signal data with the second
signal data.
[0013] According to another embodiment of the present invention,
the automatically aligning includes computing a correlation
coefficient produced by a cross-correlation algorithm using the
reference signal data and the second signal data. The automatically
aligning further includes determining whether a maximum correlation
coefficient is produced by shifting the second signal data relative
to the reference signal data and computing a correlation
coefficient produced by the cross-correlation algorithm using the
shifted second signal data and the reference signal data. The
automatically aligning further includes repeating the determining
until a maximum correlation coefficient is produced by the
cross-correlation algorithm. The cross-correlation algorithm can be
a circular or linear cross-correlation algorithm in embodiments of
the present invention.
[0014] According to various embodiments of the present invention,
the method may further include communicating an instruction to the
reference monitoring device to buffer the reference signal data for
the predetermined number of cycles. The method may further include
providing reference time data, receiving first time data from the
reference monitoring device, and synchronizing the first time data
with the reference time data. The method may further include
sampling data at the zero-crossing of a reference channel
associated with the reference monitoring device, determining
whether the values of the sampled data are zero, negative, or
positive, assigning phase notations based on the determining, and
displaying information representing the phase notations to the
user. Optionally, the user can be alerted when the phase notations
are misidentified on a phase conductor.
[0015] According to still another embodiment of the present
invention, monitoring system software sends an instruction or
message to monitoring devices in a power monitoring system to begin
buffering data (preferably data indicative of fundamental frequency
variations). The monitoring system software reads the data from
each monitoring device and selects a reference monitoring device
and another monitoring device to analyze. The data between the two
monitoring devices are cross-correlated using a circular or linear
cross-correlation algorithm, for example. The cycle count and time
relationships between the two devices are stored in a matrix. When
all devices have been analyzed and their respective data aligned
relative to one another, the monitoring system software analyzes
the voltage (or current) data for mis-wirings. If a mis-wiring is
detected, the user is notified.
[0016] According to other aspects, noisy data alignment techniques
are disclosed. A method of automatically aligning data measured by
a number, n, of monitoring devices in a power monitoring system,
comprises: receiving from each of said monitoring devices
respective signal data representing at least frequency variations
measured by respective ones of said monitoring devices, said
monitoring devices including a reference monitoring device and a
second monitoring device; correlating said signal data from said
reference monitoring device with said signal data from said second
monitoring device to determine a reference cycle count, M.sub.i,
associated with said reference monitoring device corresponding to a
maximum correlation coefficient and a second cycle count, M.sub.j,
associated with said second monitoring device corresponding to said
maximum correlation coefficient; automatically calculating a direct
cycle count offset, M.sub.ij, as a function of a difference between
said reference cycle count, M.sub.i, and said second cycle count,
M.sub.j, and storing said direct cycle count offset in a direct
cycle count offset matrix; and automatically calculating an
indirect cycle count offset as a function of at least M.sub.k,
where k.noteq.i.noteq.j and 1.ltoreq.k.ltoreq.n, said M.sub.k being
a cycle count associated with a monitoring device of said n
monitoring devices other than said reference monitoring device and
other than said second monitoring device.
[0017] The automatically calculating said indirect cycle count
offset may be carried out with respect to at least two other of
said n monitoring devices except said reference monitoring device
and except said second monitoring device to produce at least two
indirect cycle count offsets including said indirect cycle count
offset. The method may further comprise determining which of said
at least 2 indirect cycle count offsets differs from said direct
cycle count offset. The method may still further comprise:
determining a statistical mode from a set comprised of said at
least 2 indirect cycle count offsets to produce a mode value; and
determining whether the mode value differs from said direct cycle
count offset.
[0018] The method may further comprise, responsive to said direct
cycle count offset differing from said indirect cycle count offset,
producing a modified direct cycle count offset equal to said
indirect cycle count offset. The method may further comprise
storing an indication that said signal data associated with said
reference monitoring device and said signal data associated with
said second monitoring device are aligned. The method may further
comprise communicating said modified direct cycle count offset to
said reference monitoring device or to said second monitoring
device to cause said reference monitoring device or said second
monitoring device to adjust a cycle counter in said reference
monitoring device or in said second monitoring device by a value
corresponding to said modified direct cycle count offset.
[0019] The indirect indirect cycle count offset may be a function
of at least M.sub.ik-M.sub.jk. The indirect cycle count offset may
be a function of at least M.sub.m, where m.noteq.i.noteq.j and
1.ltoreq.m.ltoreq.n, said M.sub.m being a cycle count associated
with a monitoring device of said n monitoring devices other than
said reference monitoring device and other than said second
monitoring device and other than said monitoring device associated
with M.sub.k.
[0020] The method may further comprise: determining a first
verification cycle count, M.sub.i', associated with said reference
monitoring device corresponding to a first correlation coefficient
that is less than said maximum correlation coefficient; determining
a second verification cycle count, M.sub.j', associated with said
second monitoring device corresponding to said first correlation
coefficient; automatically calculating a verification cycle count
offset, M.sub.ij', based upon the difference between said first
verification cycle count, M.sub.i', and said second verification
cycle count, M.sub.j', and storing said verification cycle count
offset; and responsive to said verification cycle count offset
equaling said indirect cycle count offset, storing an indication of
a level of confidence in said indirect cycle count offset based
upon said first correlation coefficient.
[0021] The first correlation coefficient may be above a
predetermined threshold below said maximum correlation coefficient.
The direct cycle count offset matrix may be an (n.times.n)
skew-symmetric matrix. The frequency variations represented by said
first signal data may be variations in fundamental frequency or
variations in harmonic frequency, wherein said variations are
associated with a voltage or a current.
[0022] Each of the n monitoring devices may include a cycle
counter, and the method may further comprise communicating
simultaneously a signal to said n monitoring devices to reset their
respective cycle counters.
[0023] According to another aspect, a method of automatically
aligning data measured by a number, n, of monitoring devices in a
power monitoring system, comprises: receiving from each of said
monitoring devices respective signal data, S.sub.n, representing at
least frequency variations measured by respective ones of said
monitoring devices; for each of a plurality of device pairs within
a set comprising said n number of monitoring devices, wherein each
device pair is termed D.sub.ij, where i.noteq.j, where
1.ltoreq.i.ltoreq.n, and where 1.ltoreq.j.ltoreq.n, correlating
said signal data S.sub.i with said signal data S.sub.j for each of
said device pairs, D.sub.ij, to determine respective cycle counts,
M.sub.i and M.sub.j, associated with D.sub.i and D.sub.j,
respectively, said cycle counts corresponding to a maximum
correlation coefficient produced by said correlating; for each of
said device pairs, D.sub.ij, automatically calculating a direct
cycle count offset, M.sub.ij=M.sub.i-M.sub.j, and storing said
direct cycle count offset in a direct cycle count offset matrix;
for each of said direct cycle count offsets, M.sub.ij,
automatically calculating a plurality of indirect cycle count
offsets as a function of at least M.sub.k, said M.sub.k being a
cycle count associated with a monitoring device of said n
monitoring devices other than said reference monitoring device and
other than said second monitoring device, where
1.ltoreq.k.ltoreq.n, and k.noteq.i.noteq.j; storing said plurality
of indirect cycle count offsets for each M.sub.ij in an indirect
cycle count offset matrix; and for each of said direct cycle count
offsets, M.sub.ij, in said direct cycle count offset matrix,
determining whether M.sub.ij is not equal to at least one of said
plurality of indirect cycle count offsets, and, responsive thereto,
storing an indication that M.sub.ij in said direct cycle count
offset matrix is equal to a value corresponding to said at least
one of said indirect cycle count offsets.
[0024] The method may further comprise communicating an indication
of said value to D.sub.i or D.sub.j to cause D.sub.i or D.sub.j to
adjust a cycle counter by an amount corresponding to said value.
The method may further comprise communicating a signal to each of
said n monitoring devices to reset respective cycle counters in
each of said n monitoring devices at substantially the same time.
The method may further comprise: determining a statistical mode
from a set comprised of said indirect cycle count offsets for
M.sub.ij to produce a mode value; and determining whether said mode
value equals M.sub.ij in said direct cycle count offset matrix.
[0025] The correlating may produce a plurality of correlation
coefficients including said maximum correlation coefficient, and
the method may further comprise: for said devices D.sub.i and
D.sub.j corresponding to said modified M.sub.ij, determining a
plurality of probable cycle count offsets associated with a
predetermined number of said plurality of correlation coefficients
that are less than said maximum correlation coefficient; and
responsive to one of said plurality of said probable cycle count
offsets equaling said modified M.sub.ij, storing an indication of a
level of confidence in said modified M.sub.ij commensurate with how
proximal a correlation coefficient of said plurality of said
correlation coefficients corresponding to said one of said
plurality of said probable cycle count offsets is to said maximum
correlation coefficient.
[0026] The method may further comprise: receiving from at least one
of said monitoring devices second signal data representing at least
frequency variations measured by said at least one of said
monitoring devices; and adjusting a cycle count associated with
said at least one of said monitoring devices by said value
corresponding to said at least one of said indirect cycle count
offsets.
[0027] According to still another aspect, a method of automatically
aligning data monitored by a number, n, of monitoring devices, D,
associated with a power monitoring system, comprises: automatically
correlating respective signal data from a pair of said monitoring
devices, D.sub.i and D.sub.j, to determine a maximum correlation
coefficient associated with respective cycle counts for said pair
of monitoring devices, D.sub.ij, said respective signal data
representing frequency variations monitored by said D.sub.i and
said D.sub.j, respectively; determining a first cycle count offset,
M.sub.ij, by calculating a difference between said respective cycle
counts; determining a second cycle count offset from a function
that includes at least a cycle count associated with a monitoring
device of said monitoring devices other than D.sub.i or D.sub.j;
and storing an indication that said first cycle count offset is
equal to a value corresponding to said second cycle count
offset.
[0028] The method may further comprise communicating an instruction
to said D.sub.i or to said D.sub.j to adjust a cycle counter, which
stores said respective cycle counts, by an amount corresponding to
said value.
[0029] The automatically correlating may include determining
whether said second cycle count offset equals a cycle count offset
associated with a correlation coefficient that is less than said
maximum correlation coefficient.
[0030] The foregoing and additional aspects of the present
invention will be apparent to those of ordinary skill in the art in
view of the detailed description of various embodiments, which is
made with reference to the drawings, a brief description of which
is provided next.
BRIEF DESCRIPTION OF THE DRAWINGS
[0031] The foregoing and other advantages of the invention will
become apparent upon reading the following detailed description and
upon reference to the drawings.
[0032] FIG. 1 is functional block diagram of an automated data
integration monitoring system in accordance with the present
invention;
[0033] FIG. 2 is a functional block diagram of a simplified power
monitoring system;
[0034] FIG. 3 is a functional block diagram of a monitoring device
in accordance with an embodiment of the present invention;
[0035] FIG. 4 are exemplary frequency data samples from two
monitoring devices that are aligned in accordance with the present
invention;
[0036] FIG. 5A is a flow chart diagram of a data alignment
algorithm in accordance with an embodiment of the present
invention;
[0037] FIG. 5B is a flow chart diagram of a data alignment
algorithm in accordance with another embodiment of the present
invention;
[0038] FIG. 6 is a functional block diagram of a simplified
hierarchy with a single main and two feeders;
[0039] FIG. 7 is an exemplary diagram of a single radial-fed
system;
[0040] FIG. 8 is an exemplary diagram of a multiple radial-fed
system;
[0041] FIGS. 9-11A is a flow chart diagram of an auto-learned
hierarchy algorithm in accordance with an embodiment of the present
invention;
[0042] FIG. 11B is a flow chart diagram of an auto-learned
hierarchy algorithm in accordance with another embodiment of the
present invention;
[0043] FIG. 11C is a flow chart diagram of an auto-learned
hierarchy algorithm in accordance with still another embodiment of
the present invention;
[0044] FIG. 12 is a flow chart diagram of an automated integrated
monitoring algorithm in accordance with an embodiment of the
present invention;
[0045] FIG. 13 is a cross-correlation chart for an exemplary device
pair showing a number of correlation coefficients;
[0046] FIG. 14A is a flow chart diagram of a noisy data alignment
algorithm in accordance with an aspect; and
[0047] FIG. 14B is a flow chart diagram of an optional verification
algorithm to the noisy data alignment algorithm shown in FIG.
14A.
[0048] While the invention is susceptible to various modifications
and alternative forms, specific embodiments have been shown by way
of example in the drawings and will be described in detail herein.
It should be understood, however, that the invention is not
intended to be limited to the particular forms disclosed. Rather,
the invention is to cover all modifications, equivalents, and
alternatives falling within the spirit and scope of the invention
as defined by the appended claims.
DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS
[0049] Turning now to FIG. 1, an automated data integrated
monitoring system 100 is generally shown. A utility system 102
having multiple monitoring devices M provides data from each
monitoring device M that is communicated to an automated data
alignment system 104 and an automated hierarchy classification
system 106. The data is aligned automatically in the automated data
alignment system 104 in accordance with the present invention and
produces data that is aligned such that it represents the data when
it was actually seen simultaneously by the monitoring devices M in
the power monitoring system 102. The hierarchy classification
system 106 automatically learns the hierarchy of monitoring devices
present in the utility system 102 and their relationships relative
to one another.
[0050] Once the data from each monitoring device M is aligned and
each monitoring device's location is known, the data is said to be
in context 108. The contextual data 108 can be used by software
applications 110 to provide and diagnose useful information about
the utility system 102 beyond what is generally available if the
data is not in context. The utility being monitored in the utility
system 102 can be any of the five utilities designated by the
acronym, WAGES, or water, air, gas, electricity, or steam. Each
monitoring device measures characteristics of the utility, and
quantifies these characteristics into data that can be analyzed by
a computer.
[0051] A user interacts with the software applications 110 via a
conventional user interface 112. The software applications 110 can
be linked to other systems 114, such as a billing system, and use
the contextual data 108 to communicate messages between the other
systems 114 and the user interface 112.
[0052] The data alignment system 104 aligns data, such as voltage,
current, time, events, and the like, from multiple monitoring
devices M in a utility system, and is a valuable tool for users.
When data from all the monitoring devices M is aligned to the same
point in time that the data occurred, the data can be put into a
temporal context from which additional decisions regarding hardware
and software configuration can be automatically made or
recommended. As used herein, a monitoring device refers to any
system element or apparatus with the ability to sample, collect, or
measure one or more operational characteristics or parameters of a
utility system 102. When the utility system 102 is a power
monitoring system, the monitoring device M can be a meter that
measures electrical characteristics or parameters of the power
monitoring system.
[0053] The data alignment techniques (which are detailed below)
according to various aspects of the present invention accomplish at
least the following:
[0054] 1) Automated alignment of data in monitoring devices;
[0055] 2) Automated synchronization of time in monitoring
devices;
[0056] 3) Alignment of data and time in monitoring devices located
at different points on the power utility grid (where the monitoring
system software may obtain time data from the Internet or another
server); and
[0057] 4) Diagnosing misidentification or mislabeling of phases
throughout the electrical power system.
[0058] All real-world electrical signals in power systems
experience subtle variations in their frequency and amplitude over
time. This variation of the signal's frequency and amplitude are
both indeterminate and unique with respect to time. Each monitoring
device located on the same utility grid will simultaneously
experience the same frequency variations. Analysis of data from
monitoring devices that are directly linked to each other in the
hierarchy will reveal a correlation in their amplitude variations.
Analysis of both the frequency and amplitude variations of the
signal are then used to precisely align the data of one monitoring
device with respect to another device (or all the monitoring
devices to each other) in the data alignment system 104. The
details of the data alignment system 104 are discussed below.
[0059] The data alignment techniques of the present invention allow
all monitoring devices M in a power utility system hierarchy to be
aligned to the zero-crossing of all three phase voltages without
the use of additional hardware. The present invention also
anticipates potential phase shifts between various monitoring
devices, for example, those caused by certain transformer
configurations. Once the data of the monitoring devices are aligned
with each other, the system data is essentially aligned with
respect to the time it occurred, making more complex data analyses
feasible.
[0060] A simplified configuration of a power monitoring system 120
is shown in FIG. 2. The power monitoring system 120 includes a main
122 connected to a first load 124 by a first feeder and to a second
load 126 by a second feeder. Monitoring devices 128, 130 measure
electrical characteristics or parameters associated with the first
and second feeders, respectively. Each monitoring device 128, 130
is communicatively coupled to a computer 132.
[0061] The first monitoring device 128 can be a power meter (or
electric meter), such as shown in FIG. 3. The monitoring device 128
includes a controller 134, firmware 136, memory 138, a
communications interface 140, and three phase voltage conductor
connectors 142a,b,c, which connect to the V.sub.A, V.sub.B, and
V.sub.C phase voltage conductors, respectively, and are coupled to
the controller 134. Three phase current conductor connectors
143a,b,c, which connect to the I.sub.A, I.sub.B, and I.sub.C phase
current conductors, respectively, are optionally coupled to the
controller 134. The firmware 136 includes machine instructions for
directing the controller to carry out operations required for the
monitoring device. Memory 138 is used by the controller 134 to
store electrical parameter data measured by the monitoring device
128.
[0062] Instructions from the computer 132 are received by the
monitoring device 128 via the communications interface 140. Those
instructions include, according to an embodiment of the present
invention, instructions that direct the controller 134 to mark the
cycle count, to begin storing electrical parameter data, or to
transmit to the monitoring system software 132 electrical parameter
data stored in the memory 138. The electrical parameter data can
include any data acquired by monitoring devices, including any
combination of frequency variations, amplitude variations, and
phase variations.
[0063] The present invention provides an algorithm that precisely,
automatically, and temporally aligns the data from multiple
monitoring devices to the same voltage zero-crossing. Other data
alignment aspects discussed below are based on this capability. The
data alignment aspect of the present invention is facilitated by
functionality in both the monitoring device 128 and the monitoring
system software running on the computer 132, and the requirements
of each will be discussed individually. Collection and partial
analysis of data is performed in the monitoring device 128.
[0064] From the time the monitoring device 128 is energized, a
cycle count is performed of the measured voltage signals. The cycle
count is sequentially iterated with each positive voltage
zero-crossing (or, alternately, with each negative voltage
zero-crossing). As the monitoring device 128 measures both the
frequency and amplitude variations of the voltage and current from
cycle to cycle, a comparison is performed to their respective
nominal values. The frequency and amplitude variations and
associated cycle count are tracked by the device firmware 136. The
associated monitoring device time at any specified cycle count can
be stored in the memory 138.
[0065] The monitoring system software executed by the computer 132
initiates alignment of the data associated with multiple monitoring
devices by sending a global command to all monitoring devices 128,
130 on the power monitoring system 120 to mark their cycle count,
time and buffer a predetermined amount of cycle-by-cycle data.
[0066] This predetermined amount of data is established based on
the number of monitoring devices in the power monitoring system,
the communications time delays in the power monitoring system and
the magnitude of frequency and amplitude variations. When the
buffering is complete, the monitoring devices 128, 130 transmit
their buffered data to the computer 132.
[0067] Once the data is collected by the monitoring devices
128,130, the monitoring system software uploads the buffered data
for analysis. There will likely be a time offset in each monitoring
device's buffered data because the monitoring devices on the system
will likely not begin buffering the data simultaneously due to
communications time delays in the power monitoring system and
internal time delays within the monitoring devices. The buffered
data is analyzed by the monitoring system software on the computer
132 to locate the highest correlation in frequency between all the
monitoring devices 128, 130. Generally, the highest correlation is
located by sliding the buffered frequency data in one monitoring
device with respect to another until the frequency variations line
up with each other as shown in FIG. 4.
[0068] The frequency data 360 for the monitoring device 128 is
"slid" relative to the frequency data 362 for the monitoring device
130 until the frequency data for each device line up. Thus, the
zero-crossing associated with .DELTA.t.sub.1 of monitoring device
128 is aligned with the zero-crossing associated with
.DELTA.t.sub.1 of monitoring device 130, the zero-crossing
associated with .DELTA.t.sub.2 of monitoring device 128 is aligned
with the zero-crossing associated with .DELTA.t.sub.2 of monitoring
device 130, and so on. Cross-correlation algorithms for "sliding"
two data sets relative to one another until they are aligned are
discussed in further detail below in connection with FIGS. 5A and
5B.
[0069] Once the buffered data is aligned, the cycle count of the
first monitoring device 128 is associated with the cycle count of
the second monitoring device 130 in the software on the computer
132. The on-board monitoring device time may optionally also be
aligned or associated relative to one another. This process is
repeated for each monitoring device in the power monitoring system
120 until all devices' cycle counts are associated with each other.
During the data alignment process, the monitoring system software
on the computer 132 builds a matrix of each device's cycle count
and time with respect to each other and the time on the computer
132.
[0070] Although FIG. 2 shows a simplified power monitoring system
120 with just two monitoring devices 128, 130, the data alignment
embodiments of the present invention can be applied to any power
monitoring system 120 of any complexity with multiple hierarchical
levels, such as the one-line diagram shown in FIG. 7. For ease of
illustration and discussion, only two monitoring devices 128, 130
have been discussed.
[0071] Once the data of the two monitoring devices 128, 130 is
aligned relative to one another, there is typically no need to
realign the data again unless a monitoring device loses its voltage
signal or resets itself. In those cases, only the monitoring
devices that lose their voltage signal or reset need to be
realigned in accordance with the present invention. The data
alignment technique of the present invention can be initiated by an
event, such as an undervoltage or overvoltage condition, connecting
or disconnecting a load to the power monitoring system, a change in
the characteristics of the voltage, current, or a load, a
monitoring device reset, or a power loss. The data alignment
technique of the present invention can also be initiated
automatically by the monitoring software or manually by the
user.
[0072] Turning now to FIG. 5A, a flow chart, which can be
implemented as a data alignment algorithm 180 executed by the
computer 132, is shown for carrying out an embodiment of the
present invention. The data alignment algorithm 180 begins by
sending a message to the monitoring devices (such as monitoring
devices 128, 130) to begin buffering data (200) until buffering is
complete (202). The computer 132 reads the data from each device
(204). The data represents, in an embodiment, electrical parameter
data such as variations in (fundamental) frequency, variations in
amplitude, and variations in phase. Preferably, the data represents
variations in fundamental frequency. Fundamental frequency is a
preferred criterion because it remains unchanged throughout the
power monitoring system, even if transformers are present in the
system. Amplitude and phases can shift when transformers are
present in the system; however, the present invention contemplates
using amplitude and phase information as criteria.
[0073] The computer 132 selects a reference monitoring device (206)
such as monitoring device 128 and then selects a monitoring device
to analyze (208) such as monitoring device 130. Data from the
monitoring devices 128, 130 is then cross-correlated according to
the present invention (210), and each device's cycle count and time
relationships are entered into a matrix (212). The
cross-correlation is carried out by a conventional
cross-correlation algorithm, preferably such as the one provided
below in Equation 1. r .function. ( d ) = i .times. [ ( x
.function. ( i ) - mx ) * ( y .function. ( i - d ) - my ) ] i
.times. ( x .function. ( i ) - mx ) 2 .times. i .times. ( y
.function. ( i - d ) - my ) 2 ( Equation .times. .times. 1 )
##EQU1##
[0074] The correlation coefficient is represented by r(d), the
delay (offset or shift) being represented by d, where
-1<=r(d)<=1 for two series x(i) and y(i) representing the
respective data from the monitoring devices 128, 130; and mx and my
are the means of the corresponding series x(i) and y(i). According
to an embodiment, the correlation algorithm is a circular
correlation algorithm in which out-of-range indexes are "wrapped"
back within range. In another embodiment, the correlation algorithm
is a linear correlation algorithm in which each series is repeated.
In still other embodiments, the correlation algorithm is a
pattern-matching algorithm or a text-search algorithm.
[0075] After cross-correlation, the computer 132 checks whether all
monitoring devices have been analyzed (214), and if so, proceeds to
check the wiring of the phase conductors. In many instances, phase
conductors may be misidentified throughout an electrical system by
the contractor who installed them. For example, the phase that is
identified as "A-phase" at the main switchgear may be identified as
"B-phase" at the load. This nomenclature misidentification of the
phase conductors can result in confusion, and even pose a safety
hazard.
[0076] To mitigate this hazard, the computer 132 analyzes the
voltage (or current) data by sampling data at the voltage (or
current) zero-crossing of a reference channel on each monitoring
device (216). The computer 132 determines whether the wiring is
correct (218) by determining whether the values of the sampled data
are zero, negative, or positive, and, based on those values,
assigning phase notations (such as A, B, or C) for each reference
channel. If all monitoring devices are identified accurately, the
data values for Phase-A should be approximately zero. If the data
values are negative, then the phase in question is the "B-Phase"
for an ABC phase rotation. If the data values are positive, then
the phase in question is the "C-phase" for an ABC phase rotation.
The user is notified (220) whether the wiring is correct. Once the
proper phase notation is determined for each monitoring device
(222), the computer 132 may then allow the user to correct the
misidentified phase notation in any or all monitoring devices. The
phase diagnosis embodiments according to the present invention are
applicable to voltage inputs as well as current inputs.
[0077] FIG. 5B illustrates a flow chart for carrying out another
embodiment of the present invention. As with FIG. 5A, reference
will be made to the power monitoring system 120 shown in FIG. 2 for
ease of discussion, but as mentioned before, the data alignment
techniques of the present invention are applicable to any utility
monitoring system.
[0078] The computer 132 instructs each monitoring device in the
power monitoring system 120 to store data on a cycle-by-cycle basis
(250) for a predetermined number of cycles, preferably between
about 1,000 and about 10,000 cycles. When a sufficient amount of
data has been stored by the monitoring devices, the computer 132
receives the data from the monitoring devices (252) and selects a
reference monitoring device (254). Using a convention
cross-correlation algorithm such as Equation 1 above, the computer
132 calculates a correlation coefficient r(d) between at least a
portion of the data (such as about 400 cycles) of the reference
monitoring device and the data of a second monitoring device (256).
The calculated correlation coefficient is stored, and the data of
the second monitoring device is shifted relative to the reference
device by one cycle (258).
[0079] As mentioned above, the out-of-range indexes can be wrapped
back within range according to a circular correlation algorithm or
the indexes can be repeated according to a linear correlation
algorithm. A correlation coefficient is calculated using the
shifted data (260) and if no further shifts are required (262), the
data of the second monitoring device is aligned with the data of
the reference device at the point at which the maximum correlation
coefficient is calculated or at which the correlation coefficient
exceeds a threshold value, such as 0.5 (264). It should be noted
that when the correlation coefficient r(d) is close to 1.0, the
algorithm can exit without conducting any further shifts.
[0080] The computer 132 synchronizes the clocks of the second
monitoring device and the reference device at the point of
alignment (266). The computer 132 reads the cycle count in each
monitoring device and the associated monitoring device's on-board
clock time. A monitoring device's on-board clock time and cycle
count may drift with respect to each other due to the limitations
of the on-board clock. Once the data is aligned, the cycle count is
considered the absolute reference for a monitoring device. Due to
the clock drift, it may be necessary to re-read the time associated
with a device's cycle count periodically to reestablish the
device's time. The software on the computer 132 will then update
the matrix containing the monitoring device time information.
[0081] Another capability of this feature is to allow all on-board
monitoring device clocks to be periodically reset to the same value
to provide a standard time for the entire power monitoring system.
Preferably, the time within the monitoring system software (running
on the computer 132) is set according to some absolute time
reference. Once the computer time is set, the monitoring system
software resets the time on all the monitoring devices accordingly.
In this embodiment, the data and time of each monitoring device and
the software would be more accurately aligned with the absolute
time reference.
[0082] When there are no further monitoring devices to align (268),
the procedure ends. In an alternate embodiment, all of the
monitoring device's data is aligned before the clocks are
synchronized (266).
[0083] Another advantage of the data alignment techniques of the
present invention is the ability to align data and time on
different points of the utility grid. If monitoring devices are
located on two different points of the same utility grid, it is
possible to align the monitoring devices together. In this
embodiment, the monitoring devices at each geographic location are
first aligned to each other in accordance with the present
invention. The software managing all the systems is then used as
the absolute time reference for all systems, giving them all a
common point of reference.
[0084] Referring back to FIG. 1, the integrated monitoring system
100 includes the hierarchy classification system 106. Having a
thorough knowledge of an electrical power system's layout is
essential to understanding and characterizing the system. Power
meters typically provide only the electrical system's operating
parameters, but do not give information on how the parameters at
different monitoring points on the electrical system relate to each
other. Having the hierarchy of an electrical system puts the
operating parameters of multiple monitoring devices into spatial
context with each other. This spatial context gives the user a more
powerful tool to troubleshoot system problems, improve system
efficiencies, predict failures and degradation, locate the source
of disturbances, or model system responses.
[0085] The hierarchy classification system 106 of the present
invention allows the monitoring system software to collect data
from the monitoring device on the utility system 102, and
automatically determine the hierarchy of the utility system 102
with little or no user input. The level of detail given by the
hierarchy classification system 106 directly correlates with the
number and extent of monitoring devices in the utility system 102.
As supplemental monitoring devices are added, the auto-learned
hierarchical algorithm according to the present invention enables
them to be automatically incorporated into the determined
hierarchical structure.
[0086] A hierarchy of nodes is based on a relationship that
determines that one node is always greater than another node, when
the nodes are related. A hierarchy's relationship can link or
interrelate elements in one of three ways: directly, indirectly, or
not at all. An illustration of a direct link or interrelationship
is shown in FIG. 6 between the Load.sub.2 310 and Feeder.sub.2 306.
In contrast, an indirect link exists between Load.sub.2 310 and
Main.sub.1 302. Finally, there is effectively no link between the
Load.sub.1 308 and Load.sub.2 310 and between Feeder.sub.1 304 and
Feeder.sub.2 306.
[0087] In the case of a power system hierarchy, an objective is to
order elements in the power system so as to represent the true
connection layout of the power system. Determining the hierarchy of
a power system provides important information that can be used to
solve problems, increase equipment and system performance, improve
safety, and save money. The level of detail contained in a power
system hierarchy will depend on both the number of elements or
nodes that are being monitored and the node's ability to provide
feedback to the auto-learned hierarchy algorithm in the monitoring
system software running on the computer 132.
[0088] Generally, the hierarchy classification system 106 according
to the present invention utilizes an auto-learned hierarchy
algorithm in the monitoring system software that is based on rules
and statistical methods. Periodically, the monitoring system
software polls each monitoring device in the utility system 102 to
determine certain characteristics or parameters of the utility
system 102 at that node (represented by monitoring device M).
Multiple samples of specified parameters are taken from each meter
in the system at the same given point in time. Once the parameter
data is collected from each node M in the utility system 102, the
auto-learned hierarchy algorithm analyzes the data and traces the
relationships or links among the monitoring devices with respect to
the time the data sample was taken and the associated value of the
data sample. This analysis may be performed periodically to
increase the probability that the hierarchy is accurate, or to
ascertain any changes in the hierarchy. Once this iterative process
reaches some predetermined level of statistical confidence that the
determined layout of the utility system 102 is correct, the
auto-learned hierarchy algorithm ends. The final layout of the
utility system 102 is then presented to the user for concurrence.
As each monitoring device's data is evaluated over time (the
learning period) with respect to all other monitoring devices using
the auto-learned hierarchy algorithm, a basic layout of the
hierarchical structure of the utility system 102 is determined
based on the monitoring points available. In this respect, the
algorithm according to the present invention uses historical trends
of the data from each monitoring device, and those trends are
compared to determine whether any interrelationship (link) exists
between the monitoring devices. A more detailed hierarchical
structure can be determined with more monitoring points available
for analysis.
[0089] A benefit of the auto-learned hierarchy algorithm of the
present invention is to provide automatically a basic hierarchical
structure of a utility system being monitored with minimal or no
input by the user. The hierarchy can then be used as a tool for
evaluation by other systems 114. Another benefit is that the
present invention improves the accuracy of the time synchronization
between the monitoring devices and the monitoring system
software.
[0090] In an embodiment in which the utility system 102 is a power
monitoring system, samples of specific electrical parameters (such
as power, voltage, current, or the like) are simultaneously taken
from each monitoring device in the power monitoring system. This
parameter data is stored and analyzed with respect to the time the
sample is taken, the associated value of the data point, and the
monitoring device providing the data.
[0091] Data taken from each monitoring device in the power
monitoring system is compared with each other to determine whether
any correlation exists between the monitoring devices. The data is
analyzed for statistical trends and correlations as well as
similarities and differences over a predetermined period of time in
accordance with the present invention.
[0092] According to an embodiment, one or more rules or assumptions
are used to determine the hierarchical order of the power system.
Certain assumptions may have to be made about the utility system in
order to auto-learn the utility system's hierarchy. The assumptions
are based on Ohm's Law, conservation of energy, and working
experience with typical power distribution and power monitoring
systems.
[0093] General rules that may be made by the auto-learned hierarchy
algorithm in connection with power systems and power monitoring
systems may include or not include any combination of the
following:
[0094] 1. The power system being analyzed is in a single 320 (FIG.
7) or multiple radial feed configuration 330 (FIG. 8).
[0095] 2. The meter measuring the highest energy usage is assumed
to be at the top of the hierarchical structure (e.g., Main 322
shown in FIG. 7) taking into account inaccuracies in the
meters.
[0096] 3. The rate of sampling data by the meters is at least
greater than the shortest duty cycle of any load.
[0097] 4. Energy is not alternately consumed and generated on the
power system during the parameter data collection process.
[0098] 5. The error due to the offset of time in all meters on the
power monitoring system is minimal where data is pushed from the
monitoring device to the monitoring system software running on the
computer 132.
[0099] Any combination of the following additional parameters may
or may not be present for the auto-learned hierarchy algorithm:
[0100] 1. Data is not collected for hierarchical purposes from two
monitoring devices installed at the same point of a power system,
though this parameter is not necessarily a requirement in all
aspects disclosed herein.
[0101] 2. Meters with no load are ignored or only use voltage,
measurements, and/or configuration information to determine their
position in the hierarchy.
[0102] 3. Multiple mains (Main1, Main2, Main3, etc.) may exist in
the power system.
[0103] 4. Data is provided to the monitoring system software by
each monitoring device in the system.
[0104] 5. Loads that start or stop affect the load profiles for any
corresponding upstream metered data with a direct or indirect link
to that load.
[0105] 6. Voltage characteristics (fundamental, harmonic,
symmetrical components) are relatively consistent for all
monitoring devices on the same bus.
[0106] 7. Transformer losses on the electrical system are minimal
with respect to the loads downstream from the transformer.
[0107] 8. General correlation (over time) of loads between
monitoring devices indicates either a direct or indirect link.
[0108] 9. Multiple unmetered loads at a point in the power system
are aggregated into a single unknown load.
[0109] Any of the foregoing assumptions and parameters can be
combined for a radial-fed electrical power system. For example, in
a specific embodiment, any combination of the following rule-based
assumptions and parameters may or may not be utilized:
[0110] 1. Power is higher the further upstream (closer to the top
of the hierarchy) a monitoring device is, assuming no intervening
upstream transformers or other energy conversion elements.
[0111] 2. Harmonic values are generally lower the further upstream
a monitoring device is.
[0112] 3. Transformers can vary the voltages and currents.
[0113] 4. Total power flow is higher upstream than downstream.
[0114] 5. The power system may be a radial-fed system.
[0115] 6. Two monitoring devices will not be installed at the same
point, though this parameter is not necessarily a requirement in
other aspects or embodiments.
[0116] 7. Monitoring devices with the same voltage distortion are
adjacently connected.
[0117] 8. The total load measured at a specific hierarchical level
is equal (excluding losses) to the sum of all measured and
unmeasured loads directly linked to that hierarchical level.
[0118] Monitoring devices are considered to be on the same
hierarchical level if they are all directly linked to the same
reference device. For example, referring to FIG. 7, a simplified
one-line diagram of a utility monitoring system 320 is shown having
five distinct levels represented by 323a,b,c,d,e. In the specific
case of a power monitoring system, each level represents a feeder
to which multiple monitoring devices can be directly linked. All
monitoring devices directly linked to a feeder are considered to be
on the same feeder level. Thus, the main 322 is directly linked to
the feeder 323a, and thus exists on its own level in the hierarchy.
Feeder 323b directly links to three monitoring devices, and
therefore comprises another distinct level. Feeder 323c comprises
another level distinct from feeders 323a and 323b because the
monitoring devices directly linked to feeder 323c are not directly
linked to feeders 323a or 323b. In the case of a water, air, gas,
and steam systems, each level may be represented by a header
instead of a feeder.
[0119] A specific aspect of the auto-learned hierarchy algorithm
400 in accordance with an embodiment of the present invention is
flow-charted in FIGS. 9-11A. The algorithm 400 first checks whether
there is more than one monitoring device in the system (402), and
if not, the algorithm ends. If more than one monitoring device is
present, electrical data is taken from each monitoring device
(M.sub.1, M.sub.2, . . . , M.sub.k) and compiled into a Data Table
(404). The Data Table tabulates the raw data (such as power,
voltage magnitude, voltage distortion, current magnitude, current
distortion, or symmetrical component data) taken at regular
intervals (T.sub.1, T.sub.2, . . . , T.sub.n) over a given time
period. The time period between samples depends on the shortest
duty cycle of any load in the power monitoring system. The maximum
time period (T.sub.n) is determined based on the level of variation
of each monitoring device's load in the power monitoring system.
The monitoring device with the maximum power in the Data Table is
assumed to be a Main (i.e., highest level in the electrical
hierarchy) (408). However, the present invention also contemplates
multiple hierarchies (i.e., multiple Mains). An example of the Data
Table is shown in Table 1 below. TABLE-US-00001 TABLE 1 Data Table
Example Time Meter 1 Meter 2 Meter 3 Meter 4 . . . Meter k T.sub.1
D.sub.11 D.sub.21 D31 D.sub.41 . . . D.sub.k1 T.sub.2 D.sub.12
D.sub.22 D32 D.sub.42 . . . D.sub.k2 T.sub.3 D.sub.13 D.sub.23 D33
D.sub.43 . . . D.sub.k3 T.sub.4 D.sub.14 D.sub.24 D34 D.sub.44 . .
. D.sub.k4 . . . . . . . . . . . . . . . . . . . . . T.sub.n
D.sub.1n D.sub.2n D.sub.3n D.sub.4n . . . D.sub.kn
[0120] Once the data for the Data Table is accumulated, a Check
Matrix is developed. The Check Matrix is a matrix of logical
connections based on the Data Table. A zero (0) indicates that no
direct link exists between any two monitoring devices, and a one
(1) indicates that there is a possible relationship between two
monitoring devices. An exemplary Check Matrix is illustrated in
Table 2 below. In Table 2, it is assumed that no link exists
between Meter 1 and Meter 2. This is because the power measured by
Meter 1 exceeds Meter 2 in one entry of the Data Table and the
power measured by Meter 2 exceeds Meter 1 in another entry of the
Data Table. Meter 1 always correlates with itself so an NA is
placed in that cell of the Check Matrix. Only half of the Check
Matrix is required due to the redundancy of information.
TABLE-US-00002 TABLE 2 Check Matrix Example Meter 1 Meter 2 Meter 3
Meter 4 . . . Meter k Meter 1 NA 0 1 1 . . . 0 Meter 2 0 NA 1 0 . .
. 1 Meter 3 1 1 NA 0 . . . 1 Meter 4 1 0 0 NA . . . 0 . . . . . . .
. . . . . . . . . . . . . . Meter k 0 1 0 . . . NA
[0121] Once the Check Matrix is determined, the data from each
monitoring device in the Data Table is used to develop a
Correlation Coefficient Matrix (CCM) shown in Table 3 below. In the
CCM, a statistical evaluation is carried out to determine the
linear relationship of each monitoring device in the electrical
system with respect to the other monitoring devices in the matrix.
The correlation coefficient between any two monitoring devices is
determined and placed in the appropriate cell in the CCM. In the
exemplary Table 3 below, C.sub.12 is the correlation coefficient of
Meter 1 with respect to Meter 2. The higher the correlation
coefficient value is, the higher the probability that these two
monitoring devices are either directly or indirectly linked.
Conversely, the lower this number is, the lower the probability
that these two monitoring devices are directly or indirectly
linked. Equation 2 below is used to determine the correlation
coefficient between any two given monitoring devices: .rho. x , y =
Cov .function. ( x , y ) .sigma. x .times. .sigma. y ( Equation
.times. .times. 2 ) ##EQU2## where: .rho..sub.x,y is the
correlation coefficient and lies in the range of
-1.ltoreq..rho..sub.x,y.ltoreq.1; Co.nu.(x,y) is the covariance of
x and y; and .sigma..sub.x and .sigma..sub.y are the standard
deviations of x and y, respectively. Cov .function. ( x , y ) = 1 n
.times. j = 1 n .times. ( x j - .mu. y ) .times. ( y j - .mu. y ) (
Equation .times. .times. 3 ) ##EQU3## where: n is the number of
data elements in x and y, and .mu..sub.x and .mu..sub.y are the
mean values of x and y respectively.
[0122] The diagonal cells of the Correlation Matrix are all always
1 because each meter has 100% correlation with itself. Again, only
half of the Correlation Matrix is required due to the redundancy of
data (e.g., C.sub.12=C.sub.21). TABLE-US-00003 TABLE 3 Correlation
Coefficient Matrix (CCM) Example Meter 1 Meter 2 Meter 3 Meter 4 .
. . Meter k Meter 1 1 C.sub.12 C.sub.13 C.sub.14 . . . C.sub.1k
Meter 2 C.sub.21 1 C.sub.23 C.sub.24 . . . C.sub.2k Meter 3
C.sub.31 C.sub.32 1 C.sub.34 . . . C.sub.3k Meter 4 C.sub.41
C.sub.42 C.sub.43 1 . . . C.sub.4k . . . . . 1 . . . . . . . . . .
. . . Meter k C.sub.k1 C.sub.k2 C.sub.k3 C.sub.k4 . . . 1
[0123] Returning to FIG. 9, a list of meters is developed for each
level of the hierarchy under consideration. The top-most level is
assumed to be the meter with the largest power reading, which is
assumed to be a main. Once that meter is found in the Data Table
(408), the algorithm 400 places the main in a feeder level list of
the hierarchy and clears the list of monitoring devices on the
current feeder level in the hierarchy (410). In subsequent
iterations through the MAIN LOOP, the algorithm 400 places the
reference meter in the previous feeder level list of the hierarchy.
It should be understood that on the first iteration, there is no
previous level list. The algorithm 400 clears a Correlation
Reference Array (CRA) (412), and designates the main as the
reference monitoring device (414). An exemplary CRA is shown in
Table 4, below, for n iterations for a given feeder level. C.sub.51
corresponds to the correlation coefficient between meter 5 (the
reference meter) and meter 1, C.sub.52 corresponds to the
correlation coefficient between meter 5 and meter 2, and so forth.
Initially, the CRA is cleared for each feeder level, and the
algorithm 400 develops a new CRA for each feeder level by
populating each iteration column with correlation coefficients for
all meters on the current feeder level. A specific example is
explained in connection with Table 5 below.
[0124] The Correlation Coefficient Matrix (CCM) is calculated based
on the power data (416). In the first iteration, the only known
element in the hierarchy is the main, and the hierarchy is
auto-learned from the top-most feeder level down, in accordance
with some or all of the assumptions or parameters listed above.
TABLE-US-00004 TABLE 4 Correlation Reference Array (CRA) Example
Iteration Iteration Iteration Iteration Iteration Iteration 1 2 3 4
5 . . . n C.sub.51 C.sub.51 C.sub.51 C.sub.51 C.sub.51 . . .
C.sub.51 C.sub.52 C.sub.52 C.sub.52 C.sub.52 C.sub.52 . . .
C.sub.52 C.sub.53 C.sub.53 C.sub.53 C.sub.53 C.sub.53 . . .
C.sub.53 C.sub.54 C.sub.54 C.sub.54 C.sub.54 C.sub.54 . . .
C.sub.54 . . . . . . . . . . . . . . . . . . . . . C.sub.5m
C.sub.5m C.sub.5m C.sub.5m C.sub.5m . . . C.sub.5m
[0125] Continuing with FIG. 10, the algorithm 400 zeros the
correlation coefficients in the CCM for meters that have zeros in
the Check Matrix and meters that have already been found to be
connected (418). The column for the reference monitoring device is
copied from the CCM to the CRA (420). A specific example will be
explained next in connection with Table 5 below. Assume that meter
5 in the CCM is designated as the reference meter (414). The
algorithm 400 calculates the CCM based on the Data Table (416) and
zeroes the correlation coefficient(s) in the CCM for meters that
have zero in the Check Matrix and meters that have been found to be
connected (418). The column in the CCM corresponding to meter 5 is
copied into the column Iteration 1 of the CRA. Referring to Table
5, meter 11 has the highest correlation with meter 5 of 0.649, and
meter 11 is marked as connected with meter 5 for the current feeder
level.
[0126] In Iteration 2, meter 11's power is subtracted from meter
5's power in the data table, and the meter 5-11 correlation
coefficient drops to -0.048 in Iteration 2, which provides a high
degree of confidence that meter 11 is interrelated with meter 5.
Also noteworthy is that some meter's correlation coefficients trend
higher as the iterations progress. For example, the correlation
coefficients for meter 18 relative to meter 5 gradually increase
from 0.296 in Iteration 1 to 0.417 in Iteration 2 to 0.436 in
Iteration 3 to 0.525 in Iteration 4 and finally to 0.671 in
Iteration 5, which is the highest correlation coefficient among all
the meters (meter 5 correlated with itself is always 1.0, so its
correlation coefficient is ignored). This increasing trend also
provides a high degree of confidence that meter 18 is also directly
linked with meter 5, and this link is finally confirmed in
Iteration 5. The same increasing trends can be observed for meters
12 and 15, for example. In Iteration 7, none of the correlation
coefficients exceed a threshold, and the algorithm 400 proceeds to
analyze the next feeder level. By Iteration 7, the algorithm 400
has determined that meters 11, 12, 14, 15, 18, and 20 are directly
linked with meter 5. TABLE-US-00005 TABLE 5 CRA Example With
Exemplary Correlation Coefficients Iteration 1 Iteration 2
Iteration 3 Iteration 4 Iteration 5 Iteration 6 Iteration 7 5-1
0.020 -0.029 0.010 0.016 -0.037 -0.004 0.007 5-2 0.043 -0.020
-0.037 -0.009 -0.095 -0.091 -0.099 5-3 0.067 0.079 0.017 0.024
-0.052 -0.046 -0.009 5-4 0.018 -0.024 -0.038 -0.018 0.037 0.015
0.037 5-5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5-6 0.058 0.022
-0.016 -0.015 -0.035 -0.010 0.029 5-7 -0.042 -0.005 0.001 0.054
0.033 0.026 0.031 5-8 -0.034 -0.016 -0.057 -0.058 0.005 -0.034
-0.049 5-9 0.418 0.386 0.308 0.292 0.189 0.099 0.136 5-10 0.022
0.077 0.016 0.014 -0.016 -0.018 0.022 5-11 0.649 -0.048 -0.090
-0.095 -0.076 -0.077 -0.014 5-12 0.344 0.506 0.628 0.725 0.047
-0.007 0.016 5-13 -0.038 -0.036 0.038 0.017 -0.046 -0.023 -0.010
5-14 0.483 0.591 0.072 0.044 0.066 -0.006 0.004 5-15 0.043 0.161
0.210 0.263 0.417 0.587 0.031 5-16 0.024 0.045 0.055 0.044 -0.017
-0.010 0.022 5-17 -0.057 -0.063 -0.101 -0.090 -0.061 -0.048 -0.049
5-18 0.296 0.417 0.436 0.525 0.671 0.113 0.165 5-19 -0.046 -0.053
-0.057 -0.047 -0.046 -0.050 -0.034 5-20 0.398 0.549 0.633 0.128
0.069 0.054 0.061 5-21 -0.060 -0.017 0.028 0.080 -0.013 0.010
0.005
[0127] Still referring to FIG. 10, the algorithm 400 finds the
monitoring device (feeder) in the CRA that has the highest
correlation with the reference monitoring device (422). If the
correlation does not exceed a threshold (0.5 in a preferred
embodiment), the algorithm 400 continues to FIG. 11A (OP3), such as
in the case of Iteration 7 in Table 5 shown above.
[0128] Otherwise, the algorithm 400 determines whether the current
iteration is the first iteration for the reference monitoring
device (426), and if not, determines whether the feeder correlation
is trending higher (428). If the feeder correlation is not trending
higher, the algorithm 400 continues to FIG. 11A (OP3). A higher
trend is an indication that the monitoring device is likely on the
current level of the hierarchy under consideration.
[0129] If the current iteration is the first iteration for the
reference monitoring device, the feeder is added to the list of
monitoring devices on the current level of the hierarchy (430), and
the algorithm 400 continues to FIG. 11A (OP2). The reference
monitoring device and the feeder are designated as directly linked
(or interrelated) in a connection table (446), and the power
associated with the feeder is subtracted from the reference
monitoring device in the data table (448). The connection table
maintains a list of devices and their interrelationships (for
example, whether they are directly linked). By subtracting the
power of the feeder associated with the highest correlation
coefficient relative to the reference monitoring device, other
feeders (monitoring devices) connected to the reference monitoring
device will see their correlation coefficients increase. The
algorithm 400 returns to the FEEDER LOOP of FIG. 9, and the next
iteration continues with the remaining monitoring devices.
[0130] Turning now to the OP3 function, the algorithm 400
determines whether all monitoring devices on the previous level
have been analyzed (432), and if not, the next monitoring device
(feeder) is obtained on the previous level, and the algorithm 400
returns to the FEEDER LOOP of FIG. 9. If all monitoring devices on
the previous level have been analyzed, the algorithm 400 checks
whether a connection has been found for all monitoring devices in
the hierarchy (434). If so, the algorithm 400 exits. If not, the
algorithm 400 checks whether the highest correlation coefficient in
the CCM exceeds a threshold (436). If not, the algorithm 400 exits.
If so, the algorithm 400 determines whether any more monitoring
devices are found for the current level (438). If not, the
algorithm 400 returns to the MAIN LOOP in FIG. 9. If so, the
algorithm moves the monitoring devices on the current level to the
previous level (440) and clears the CRA (442). The algorithm
returns to the FEEDER LOOP of FIG. 9 to determine the relationships
among the remaining monitoring devices on the current level.
[0131] An auto-learned hierarchy algorithm 500 according to another
embodiment of the present invention is illustrated in FIG. 11B. The
algorithm 500 starts by receiving from each monitoring device a
criterion associated with each monitoring device (502). The
criterion can be an electrical parameter, such as power, voltage,
current, current distortion, voltage distortion, or energy, or a
parameter associated with any WAGES utility, such as volume (BTU,
MBTU, gallons, cubic feet) per unit time. The monitoring devices
can be power monitoring devices. For example, when the criterion is
a voltage distortion, monitoring devices on the same level of the
hierarchy will have roughly the same voltage distortion.
Additionally or alternatively, the algorithm can use the harmonic
distortion values to verify the hierarchy determined by the
correlations based on power criteria. Harmonic distortion can also
be used by the algorithm to better predict unknown candidates with
greater accuracy. For example, a monitoring device may be
marginally correlated with a reference device such that the
algorithm cannot determine whether a direct link exists or not.
Harmonic distortion can rule in or rule out a potential
interrelationship depending upon the harmonic distortion values of
the neighboring devices on the same level as the monitoring device
in question. For example, a different harmonic distortion returned
for the monitoring device in question could rule it out as being
directly linked with a device on the previous level.
[0132] The algorithm 500 calculates a correlation coefficient
between a reference monitoring device and every other monitoring
device to be interrelated in the hierarchy (504). The algorithm 500
determines the highest correlation coefficient (506) and
interrelates the monitoring device associated with the highest
correlation coefficient and the reference monitoring device (508).
The algorithm 500 checks whether more monitoring devices are to be
interrelated (510), and if not, the algorithm 500 ends. If so, the
algorithm 500 checks whether to use the same reference monitoring
device (512), and if so, recalculates the correlation coefficients
(504). Otherwise, the algorithm 500 selects a new reference
monitoring device (514), and recalculates the correlation
coefficients (504).
[0133] An auto-learned hierarchy algorithm 550 according to still
another embodiment of the present invention is illustrated in FIG.
11C. The algorithm 550 starts by receiving electrical parameter
data from each monitoring device at periodic time intervals (552).
The algorithm 550 arranges the electrical parameter data into a
data table that tabulates the parameter data at each time interval
(554). A correlation matrix is formed that includes correlation
coefficients between combination pairs of monitoring devices (556).
The algorithm 550 identifies an interrelationship between a
combination pair (558) and removes from the data table the power
associated with the monitoring device for which an
interrelationship was identified (560). If no more
interrelationships are to be identified (562), the algorithm 550
ends. Otherwise, it recalculates correlation coefficients among the
remaining combination pairs (564) and identifies another
interrelationship between the remaining combination pairs (558).
This process is repeated until all interrelationships among the
monitoring devices have been identified.
[0134] The auto-learned hierarchy algorithm according to the
various embodiments of the present invention is operable in both
radial-fed and multiple radial-fed systems. In multiple radial-fed
systems, the algorithm first determines the main meter having the
highest power, then determines the hierarchy for that system first
before proceeding to the next system(s) having lower power
ratings.
[0135] The auto-learned hierarchy algorithm has been discussed in
various embodiments in which the hierarchy is developed from the
top-most level towards the bottom-most level. In an alternate
embodiment, an auto-learned hierarchy algorithm develops a
hierarchy from the bottom-most level based on events local to each
level. For example, monitoring devices proximate to an event will
`see` an event, such as a load turning on or off, before monitoring
devices remote from the event will see it. The algorithm recognizes
interrelationships among monitoring devices based on the
occurrences of events and the timestamps associated with each
monitoring device as to when it became aware of an event. By
mapping out a chronology of when each monitoring device in the
system perceives an event, conclusions can be automatically drawn
based upon the time order in which monitoring device perceived that
event as to which meters are interrelated (directly linked).
[0136] Referring back to FIG. 1, the automated data integrated
monitoring system 100 produces contextual data 108 from the data
alignment system 104 and the hierarchy classification system 106.
The contextual data 108 contains the data from each monitoring
device in context with every other monitoring device and is thus
more valuable to the user. Contextual analysis of the measured data
can be performed, which involves an assessment of the data such
that specific external parameters from each monitoring device are
aligned or are made known. The primary external parameters of
concern include:
[0137] The temporal position of each monitoring device's data in
the utility system 102 relative to every other monitoring device's
data in the utility system 102; and
[0138] The spatial position of each monitoring device M in the
utility system 102 with respect to every other monitoring device M
in the utility system 102.
[0139] Evaluating all the monitoring data accumulated from the
utility system 102 in context will provide a degree of knowledge
about the utility system 102 that heretofore was unavailable.
Because the information from the entire system (software and
monitoring devices) is integrated together through a uniform
context, this approach to monitoring a utility system is referred
to as Integrated Monitoring (IM).
[0140] A useful analogy of the IM approach according to the present
invention is the central nervous system of the human body. The
brain (software) knows what is going on with the entire body (the
monitoring devices) relative to time and position. If a toe is
stubbed, the brain sends a signal for the body to react in some
manner. Similarly if an electrical event occurs, the IM algorithms
executed by the monitoring system software provides useful
information to the user on the symptoms throughout the monitored
system, potential sources of the problem, and possible solutions or
recommendations.
[0141] The present invention involves integrating data based on
analysis of the data from each monitoring point using special
algorithms (for example, a data alignment algorithm and an
auto-learned hierarchy algorithm) in the monitoring system
software. In the data alignment system 104, subtle but measurable
changes in the data's frequency and amplitude are analyzed from all
data sources. These changes are used to establish both the common
point of data alignment for all data sources and a data source's
position in the electrical system with respect to other data
sources. Because the process of integrating the system data is
performed automatically on algorithms in the monitoring system
software, much of the effort and expense required by the user is
eliminated. More arbitrary and substantial variations of the
parameters being analyzed offers quicker integration of the system
data.
[0142] There are several benefits associated with IM that are
beyond what is presently available including:
[0143] The automated IM approach greatly reduces the existing
requirements for the user to manually provide detailed information
about the power system layout in order to put the system data into
context. The IM algorithms analyze data from each monitoring point
in the electrical system to automatically determine the system
layout with little or no user involvement, saving the user time and
resources.
[0144] The automated IM approach eliminates the need for special
hardware, additional data lines, and, in some cases, monitor
accessories. The IM algorithms analyze data from each monitoring
point in the electrical system to automatically determine the
temporal alignment of the system data, saving the user equipment
and labor costs.
[0145] The automated IM approach allows an easier configuration of
monitoring hardware and software. This is because the IM algorithms
automatically put the monitoring information into context
throughout the system. Once the monitoring devices are in context,
additional decisions regarding hardware and software configuration
can automatically be made by the IM algorithms. One example would
be setting a monitoring device's under-voltage threshold depending
on the monitoring device's location within the electrical system.
Again, the automated IM approach saves the user time and
resources.
[0146] An automated IM algorithm 600 according to an embodiment of
the present invention is illustrated in FIG. 12. The algorithm 600
starts by sending a command to the monitoring devices to collect
frequency data (602). Data from the monitoring devices is uploaded
to the host computer (604) and the data from all the monitoring
devices is aligned (606) in accordance with the present invention.
When all the data is aligned, the algorithm 600 determines whether
the power system layout is complete (610). If so, the algorithm 600
ends, and the contextual data can be used in further software
applications.
[0147] If the power system layout is not complete, the algorithm
600 sends a command to the monitoring devices to collect power data
(612). The host computer running the algorithm 600 uploads the
power data from monitoring devices (614) and determines the power
system layout (616) in accordance with the present invention. This
procedure is repeated until the power system layout is complete
(618) at which point the algorithm ends.
Challenges of Aligning Multiple Devices
[0148] Empirical data has shown that while alignment between many
device pairs is obtainable, alignment between other device pairs
can be more challenging. Two devices (a device pair) that are
difficult to align with each other are said to have a "noisy"
relationship. One approach for solving these noisy meter
relationships was to take multiple data samples from the device
pair in question and pass these samples through the data alignment
algorithm described above. Once a given number of samples are taken
from the noisy device pair, the conclusions from each pass are
analyzed to determine the most consistent answer (i.e., the
statistical mode). It should be noted that the conclusions from
this technique include the probable cycle count offset between a
device pair and the ratio of the highest correlation to the second
highest correlation from a device pair. There are several
shortcomings to this approach: (1) it may still provide an
incorrect answer; (2) data must be collected multiple times from
the questionable device pair making the entire data alignment
process take longer; (3) the communications network experiences
much heavier traffic due to the larger amounts of data that must be
repeatedly passed between the devices and the software; and (4) it
is difficult to determine how many data samples are enough to
provide an accurate solution.
[0149] It became apparent that a solution needed to be found to
increase the robustness of the data alignment algorithm discussed
above where noisy device pair relationships were involved. For
convenience only, the aspects, techniques, methods, algorithms, and
implementations discussed below in connection with aligning "noisy"
devices shall be referred to as "the noisy data alignment"
algorithm. This phrase may also be variously referred to herein as
an implementation, a method, a process, a technique, a solution, or
an aspect. It is expressly understood that this phrase is merely
for convenience only and the selected terms in the phrase are not
intended to limit the aspects disclosed herein in any manner. An
example of a noisy data alignment algorithm 1400 is shown in FIG.
14A, which may be part of the data alignment system 104.
[0150] The noisy data alignment techniques disclosed below are
directed to satisfying these and other needs and solving these and
other problems. Advantages of these techniques include: (1) reduces
(or even eliminates) additional operations of the data alignment
algorithm; (2) provides a solution for "noisy" meter relationships;
(3) increases the robustness of the data alignment algorithm; and
(4) increases the overall speed and efficiency of the data
alignment process. Additional advantages and results are set forth
elsewhere herein.
Direct and Indirect Relationships in the Cycle Count Offset
Matrix
[0151] As previously stated, each device that evaluates signals on
an interconnected electrical grid experiences frequency deviations
synchronously with every other device on the grid because frequency
changes are reflected across the entire grid. Therefore, the cycle
count of each device is an integer multiple of cycles apart from
every other device's cycle count at any given time. The cycle count
offset (or difference) between each device pair varies depending on
when each device's cycle count was initiated with respect to the
other devices. The data alignment algorithm 180 disclosed above
determines the cycle count offset between any two devices.
[0152] The noisy data alignment solution provides an unexpected
improvement over the data alignment algorithm 180 because it was
empirically discovered that the concept of cycle count
relationships between discrete devices can be expanded to include
indirect cycle count relationships over the entire monitoring
system. Each system has its own unique solution that can be solved
much like solving a puzzle. By exploiting the indirect cycle count
relationships, the noisy data alignment techniques automatically
find a unique solution between "noisy" device pairs that provides a
very high degree of confidence if not total confidence in the
relationship.
[0153] As used hereinafter, a monitoring device is designated by
the letter D, and the subscript refers to a unique monitoring
device within a monitoring system. The letter M refers to a cycle
count and its subscript refers to the monitoring device with which
the cycle count is associated. D.sub.ij refers to a device pair,
where i and j refer to distinct monitoring devices in the
monitoring system and 1.ltoreq.i.ltoreq.n and 1.ltoreq.j.ltoreq.n
and i.noteq.j. The monitoring system has a number, n, of monitoring
devices that are capable of communicating signal data indicative of
frequency variations to the data alignment system 104. M.sub.ij
refers to a cycle count offset (or difference) associated with a
device pair, D.sub.ij. M.sub.k refers to a cycle count associated
with a device other than D.sub.i and other than D.sub.j.
[0154] The direct cycle count offset (M.sub.i, M.sub.j) between a
device pair (D.sub.i, D.sub.j) can be determined directly by the
following equations: M.sub.ij=M.sub.i-M.sub.j (Equation 4);
M.sub.ji=M.sub.j-M.sub.i (Equation 5); M.sub.ij=-M.sub.ji (Equation
6),
[0155] where M.sub.i is the cycle count of one device D.sub.i and
M.sub.j is the cycle count of another device D.sub.j (both taken
synchronously). For example, if M.sub.1 has a cycle count of 20 and
M.sub.2 has a cycle count of 25, then the direct cycle count offset
between the two devices (i.e., the device pair), M.sub.12, equals
-5 (note that M.sub.21 will equal +5). When i=j, the direct cycle
count offset is always zero because the equation is calculating the
offset of a device with itself. Hence, the diagonal of direct cycle
count offset matrices is always equal to zero. TABLE-US-00006 TABLE
6 Direct Cycle Count Offset Matrix Construct M.sub.1 M.sub.2
M.sub.3 M.sub.4 . . . M.sub.j M.sub.1 0 M.sub.12 M.sub.13 M.sub.14
(-) . . . M.sub.1j M.sub.2 M.sub.21 0 M.sub.23 M.sub.24 (-) . . .
M.sub.2j M.sub.3 M.sub.31 M.sub.32 0 M.sub.34 (-) . . . M.sub.3j
M.sub.4 M.sub.41 M.sub.42 M.sub.43 0 (-) . . . M.sub.4j . . . . . 0
. . . . . . . . . . . . . M.sub.i M.sub.i1 M.sub.i2 M.sub.i3
M.sub.i4 . . . 0
[0156] A Cycle Count Offset Matrix is built by entering the cycle
count offset of each device with respect to every other device on
the monitoring system using Equations 4-6 (1402). Table 6
illustrates the construction of a direct cycle count offset matrix.
All of the rows and columns correspond to every capable device in
the power monitoring system. Again, the elements in the matrix's
diagonal are equal to zero because the cycle count offset between
any device and itself is equal to zero.
[0157] All cycle count offset matrices are in the form of a
skew-symmetric matrix. In linear algebra, a skew-symmetric (or
anti-symmetric) matrix is a square matrix A whose transpose is also
its negative; that is, it satisfies the equation: A.sup.T=-A
(Equation 7)
[0158] In component form, A=(.alpha..sub.ij) where
.alpha..sub.ij=-.alpha..sub.ji for all i and j. All main diagonal
entries of a skew-symmetric matrix have to be zero, and so the
trace is zero. Thus, the cycle count offset matrix can be of the
skew-symmetric matrix type.
[0159] Because the cycle counts for all devices in a power
monitoring system 120 increment together as explained above, the
cycle count offsets between any device pair will be constant.
Therefore, the cycle count offset matrix is both fixed or constant
and unique for any given power monitoring system (provided that no
device resets occur while the noisy data alignment algorithm is
operating). If a device or devices are reset while the noisy data
alignment algorithm 1400 is operating, the algorithm 1400 will note
the reset(s) and reinitiate itself to create a new direct cycle
count offset matrix (1402), which is fixed/constant and unique.
[0160] By exploiting the concepts relating to the data alignment
algorithm 180 and the breakthrough discovery that the cycle count
offset matrix is fixed/constant (the cycle counts from all devices
increment together) and unique (there is only one correct
solution), the solution of M.sub.ij can be derived based upon the
cycle count offset relationships of multiple devices. In short, it
is possible to deduce the cycle count offset between M.sub.ij by
analyzing the cycle count offset relationships between M.sub.ik and
M.sub.jk (and M.sub.ki and M.sub.kj). Furthermore, the intrinsic
nature of the cycle count offset matrix necessitates that M.sub.ij
can be accurately determined by a multitude of unique combinations
of the cycle count offset relationships, being limited only by the
size of the matrix (n.times.n). So, the cycle count offset between
a device pair can be arrived at directly by determining the
relationship between any two given devices (M.sub.ij) or indirectly
by incorporating the relationships between other devices
(M.sub.ik-M.sub.jk, etc.).
[0161] Table 7 illustrates an exemplary direct cycle count offset
matrix in skew-symmetric form with exemplary data taken from 6
devices, resulting in a 6.times.6 matrix. The data in each cell of
the matrix is the direct cycle count offset between every
combination of device pairs. For example, cell M.sub.12 is equal to
2, so M.sub.1's cycle counter is two cycles ahead of M.sub.2's
cycle counter. Symmetrically, cell M.sub.21 is equal to -2 because
M.sub.2's cycle counter is two cycles behind M.sub.1's cycle
counter (see Equation 6). TABLE-US-00007 TABLE 7 Direct Cycle Count
Matrix (Example 1) M.sub.1 M.sub.2 M.sub.3 M.sub.4 M.sub.5 M.sub.6
M.sub.1 0 2 -4 -7 -7 -7 M.sub.2 -2 0 -6 -9 -9 -9 M.sub.3 4 6 0 -3
-3 -3 M.sub.4 7 9 3 0 0 0 M.sub.5 7 9 3 0 0 0 M.sub.6 7 9 3 0 0
0
[0162] In this example, the determination of M.sub.12 (and
M.sub.21) was derived through the direct relationship of M.sub.1
and M.sub.2. However, it is also possible to determine the cycle
count offset relationship between M.sub.1 and M.sub.2 indirectly
using other cells in the cycle count matrix with the following
equation: M.sub.ij=M.sub.ik-M.sub.jk where k.noteq.i.noteq.j
(Equation 8)
[0163] Additional indirect relationships can be derived based upon
2 to n-1 device pairs for an n.times.n cycle count offset matrix.
While the number of direct relationships is always 1 for any given
device pair, the number of indirect relationships that can be
derived is based on the size of the n.times.n matrix.
[0164] To illustrate, cell M.sub.12 from Table 7 can be determined
indirectly by finding the difference between two direct cycle count
offsets, M.sub.13 and M.sub.23:
M.sub.12=M.sub.13-M.sub.23=(-4)-(-6)=2 Cell M.sub.12 from Table 7
can also be determined indirectly by finding the difference between
three direct cycle count offsets, M.sub.13, M.sub.43, and M.sub.42:
M.sub.12=M.sub.13-M.sub.43-M.sub.24=(-4)-(3)-(-9)=2
[0165] In this example, up to 5 device pair relationships (n-1
where n=6) may be used to derive the cycle count offset for
M.sub.12. One example of deriving M.sub.12 from 5 device pair
relationships is:
M.sub.12=M.sub.13-M.sub.43-M.sub.54-M.sub.65-M.sub.26=(-4)-(3)-(0)-(0)-(--
9)=2 It should be noted that there are numerous unique combinations
of device pair relationships that can be used to indirectly derive
the cycle count offset for a given device pair.
[0166] Table 8 illustrates dozens of unique combinations of
equations that can be derived from the relationships in a given
sized (in this case, 6.times.6) cycle count offset matrix. It
should be readily apparent that systems with more monitoring
devices have a proportionally larger number of unique combinations
that can be derived compared to systems with fewer monitoring
devices. TABLE-US-00008 TABLE 8 Sample Direct and Indirect Cycle
Count Offset Equations for Table 7 Device Relationship Pair
Equation Result Type M.sub.12 = M.sub.1 - M.sub.2 2 Direct M.sub.12
= M.sub.13 - M.sub.23 2 Unique indirect M.sub.12 = M.sub.14 -
M.sub.24 2 relationships derived M.sub.12 = M.sub.15 - M.sub.25 2
from two sets of M.sub.12 = M.sub.16 - M.sub.26 2 device pairs
M.sub.12 = M.sub.13 - M.sub.43 - M.sub.24 2 Unique indirect
M.sub.12 = M.sub.13 - M.sub.53 - M.sub.25 2 relationships derived
M.sub.12 = M.sub.13 - M.sub.63 - M.sub.26 2 from three sets of
M.sub.12 = M.sub.14 - M.sub.34 - M.sub.23 2 device pairs M.sub.12 =
M.sub.14 - M.sub.54 - M.sub.25 2 M.sub.12 = M.sub.14 - M.sub.64 -
M.sub.26 2 M.sub.12 = M.sub.15 - M.sub.35 - M.sub.23 2 M.sub.12 =
M.sub.15 - M.sub.45 - M.sub.24 2 M.sub.12 = M.sub.15 - M.sub.65 -
M.sub.26 2 M.sub.12 = M.sub.16 - M.sub.36 - M.sub.23 2 M.sub.12 =
M.sub.16 - M.sub.46 - M.sub.24 2 M.sub.12 = M.sub.16 - M.sub.56 -
M.sub.25 2 M.sub.12 = M.sub.13 - M.sub.43 - M.sub.54 - M.sub.25 2
Unique indirect M.sub.12 = M.sub.13 - M.sub.43 - M.sub.64 -
M.sub.26 2 relationships derived M.sub.12 = M.sub.13 - M.sub.53 -
M.sub.54 - M.sub.24 2 from four sets of M.sub.12 = M.sub.13 -
M.sub.53 - M.sub.56 - M.sub.26 2 device pairs M.sub.12 = M.sub.13 -
M.sub.63 - M.sub.64 - M.sub.24 2 M.sub.12 = M.sub.13 - M.sub.63 -
M.sub.65 - M.sub.25 2 M.sub.12 = M.sub.14 - M.sub.34 - M.sub.53 -
M.sub.25 2 M.sub.12 = M.sub.14 - M.sub.34 - M.sub.63 - M.sub.26 2
M.sub.12 = M.sub.14 - M.sub.54 - M.sub.35 - M.sub.23 2 M.sub.12 =
M.sub.14 - M.sub.54 - M.sub.56 - M.sub.26 2 M.sub.12 = M.sub.14 -
M.sub.64 - M.sub.36 - M.sub.23 2 M.sub.12 = M.sub.14 - M.sub.64 -
M.sub.65 - M.sub.25 2 M.sub.12 = M.sub.15 - M.sub.35 - M.sub.43 -
M.sub.24 2 M.sub.12 = M.sub.15 - M.sub.35 - M.sub.63 - M.sub.26 2
M.sub.12 = M.sub.15 - M.sub.45 - M.sub.34 - M.sub.23 2 M.sub.12 =
M.sub.15 - M.sub.45 - M.sub.64 - M.sub.26 2 M.sub.12 = M.sub.15 -
M.sub.65 - M.sub.36 - M.sub.23 2 M.sub.12 = M.sub.15 - M.sub.65 -
M.sub.46 - M.sub.24 2 M.sub.12 = M.sub.16 - M.sub.36 - M.sub.53 -
M.sub.25 2 M.sub.12 = M.sub.16 - M.sub.36 - M.sub.43 - M.sub.24 2
M.sub.12 = M.sub.16 - M.sub.46 - M.sub.34 - M.sub.23 2 M.sub.12 =
M.sub.16 - M.sub.46 - M.sub.54 - M.sub.25 2 M.sub.12 = M.sub.16 -
M.sub.56 - M.sub.35 - M.sub.23 2 M.sub.12 = M.sub.16 - M.sub.56 -
M.sub.45 - M.sub.24 2 M.sub.12 = M.sub.13 - M.sub.43 - M.sub.54 -
M.sub.65 - M.sub.26 2 Unique indirect M.sub.12 = M.sub.13 -
M.sub.43 - M.sub.64 - M.sub.56 - M.sub.25 2 relationships derived
M.sub.12 = M.sub.13 - M.sub.53 - M.sub.65 - M.sub.46 - M.sub.24 2
from five sets of M.sub.12 = M.sub.13 - M.sub.53 - M.sub.45 -
M.sub.64 - M.sub.26 2 device pairs M.sub.12 = M.sub.13 - M.sub.63 -
M.sub.46 - M.sub.54 - M.sub.25 2 M.sub.12 = M.sub.13 - M.sub.63 -
M.sub.56 - M.sub.45 - M.sub.24 2 M.sub.12 = M.sub.14 - M.sub.34 -
M.sub.53 - M.sub.65 - M.sub.26 2 M.sub.12 = M.sub.14 - M.sub.34 -
M.sub.63 - M.sub.56 - M.sub.25 2 M.sub.12 = M.sub.14 - M.sub.54 -
M.sub.65 - M.sub.36 - M.sub.23 2 M.sub.12 = M.sub.14 - M.sub.54 -
M.sub.35 - M.sub.63 - M.sub.26 2 M.sub.12 = M.sub.14 - M.sub.64 -
M.sub.56 - M.sub.35 - M.sub.23 2 M.sub.12 = M.sub.14 - M.sub.64 -
M.sub.36 - M.sub.53 - M.sub.25 2 M.sub.12 = M.sub.15 - M.sub.35 -
M.sub.43 - M.sub.64 - M.sub.26 2 M.sub.12 = M.sub.15 - M.sub.35 -
M.sub.63 - M.sub.46 - M.sub.24 2 M.sub.12 = M.sub.15 - M.sub.45 -
M.sub.34 - M.sub.63 - M.sub.26 2 M.sub.12 = M.sub.15 - M.sub.45 -
M.sub.64 - M.sub.36 - M.sub.23 2 M.sub.12 = M.sub.15 - M.sub.65 -
M.sub.46 - M.sub.34 - M.sub.23 2 M.sub.12 = M.sub.15 - M.sub.65 -
M.sub.56 - M.sub.45 - M.sub.24 2 M.sub.12 = M.sub.16 - M.sub.36 -
M.sub.43 - M.sub.54 - M.sub.25 2 M.sub.12 = M.sub.16 - M.sub.36 -
M.sub.53 - M.sub.45 - M.sub.24 2 M.sub.12 = M.sub.16 - M.sub.46 -
M.sub.54 - M.sub.35 - M.sub.23 2 M.sub.12 = M.sub.16 - M.sub.46 -
M.sub.34 - M.sub.53 - M.sub.25 2 M.sub.12 = M.sub.16 - M.sub.56 -
M.sub.45 - M.sub.34 - M.sub.23 2 M.sub.12 = M.sub.16 - M.sub.56 -
M.sub.35 - M.sub.43 - M.sub.24 2
Innovative Approach to Solving the Noisy Device Pair
Relationship
[0167] The fact that there are so many relationships (both direct
and indirect) for each device pair AND that only one unique
solution exists for the direct cycle count offset matrix provides
the foundation for the noisy data alignment techniques herein to
determine which devices are noisy and to find a solution
notwithstanding the noisy relationships. Importantly, where
previously data had to be collected multiple times in an attempt to
statistically determine the cycle count offsets of discrete device
pairs, the noisy data alignment solution herein can confidently
determine the entire direct cycle count offset matrix in many cases
using only a single data collection pass and iterate to the
solution where noisy meters are present. TABLE-US-00009 TABLE 9
Exemplary Device List for Testing Device Number Device Type IP*
Serial Address M.sub.1 CM4000T 158.197.126.27 1 M.sub.2 CM4250
158.197.126.17 1 M.sub.3 CM4000 158.197.126.17 2 M.sub.4 CM4250
158.197.148.21 1 M.sub.5 CM4000T 158.197.148.21 2 M.sub.6 CM3350
158.197.148.21 3
[0168] To illustrate this noisy data alignment technique, Table 9
lists six exemplary devices commercially available from Square D
Company that were tested. These devices were split into three
groups and interconnected to the software via Ethernet and
daisy-chained RS-485 communications networks. There are a total of
fifteen unique combinations of device pairs based on the following
equation: Number .times. .times. of .times. .times. Unique .times.
.times. Device .times. .times. Parts = n .function. ( n - 1 ) 2 (
Equation .times. .times. 9 ) ##EQU4## where n is the number of
devices.
[0169] Table 10 shows each unique device pair for the exemplary
six-device system. The data alignment algorithm 180 was initiated
for the six devices and the direct cycle count offsets based on the
direct relationships (i.e., the difference between the
corresponding cycle counts from each device were determined at the
point of the highest correlation coefficient produced by the
cross-correlation of signal data from device pairs) were determined
for each unique combination of device pairs. It should be readily
apparent that no firm conclusions can be drawn from Table 10
regarding its correctness. The data alignment algorithm 180 can
only reinitiate and generate multiple instances of the data in
Table 10. Statistical analysis would then be carried out to
ascertain the most probable cycle count offset for each device
pair. TABLE-US-00010 TABLE 10 Direct Cycle Count Offset Table
Produced by Data Alignment Algorithm All Combinations of Device
Pair Cycle Count Offsets M.sub.12 M.sub.13 M.sub.14 M.sub.15
M.sub.16 M.sub.23 M.sub.24 M.sub.25 M.sub.26 M.sub.34 M.sub.35
M.sub.36 M.sub.45 M.sub.46 M.sub.56 2 -4 -7 -7 -247 -6 -9 -9 -249
-3 -3 -3 0 0 0
[0170] The noisy data alignment algorithm collects the results of
each device pair cycle count offset from Table 10 and constructs
the cycle count offset matrix shown in Table 11, which is a
compilation of the direct cycle count offset relationships of each
device pair in the matrix form. TABLE-US-00011 TABLE 11 Direct
Cycle Count Offset Matrix (Initial Data) Device M.sub.1 M.sub.2
M.sub.3 M.sub.4 M.sub.5 M.sub.6 M.sub.1 0 2 -4 -7 -7 -247 M.sub.2
-2 0 -6 -9 -9 -249 M.sub.3 4 6 0 -3 -3 -3 M.sub.4 7 9 3 0 0 0
M.sub.5 7 9 3 0 0 0 M.sub.6 247 249 3 0 0 0
[0171] Using the concepts outlined above, a new indirect cycle
count offset table is constructed for the indirect cycle count
offset relationships (see Table 12) (1404). For the sake of
simplicity, Table 12 only includes each of the indirect
relationships using two sets of unique device pairs; however, all
indirect relationships up to 5 sets of unique device pairs may be
used in this example (refer to Table 8 for other unique device
pairs for a six-device system). It is not necessary to determine
indirect relationships for every combination of device pairs. It
suffices to determine indirect relationships for suspect device
pairs, such as device pairs whose standard deviation from the mean
exceed a threshold when the cycle counters for all of the devices
have been reset to the same initial value (typically 0)
pseudo-synchronously. In Table 11, suspect pairs include M.sub.61
and M.sub.62 (and their corresponding device pairs, M.sub.16 and
M.sub.26) as these device pairs have cycle count offsets that
deviate strongly from the mean cycle count offsets of other device
pairs.
[0172] The cycle count offset matrix is a 6.times.6 matrix because
there are six devices. There are only four unique indirect
equations using two sets of device pairs to solve for each device
pair, and each is shown in Table 12. Again, the cells in the matrix
diagonal are equal to zero because a device cannot be offset from
itself. The algorithm 1400 compares the direct relationship data
from the direct cycle count offset matrix and the indirect
relationship results from the indirect cycle count offset matrix
for each unique device pair to each other (1406). In various
aspects, the algorithm 1400 may make this comparison for every
device pair or for a subset of device pairs, such as those device
pairs whose indirect relationships are suspect. Examples are
provided below.
[0173] As can be seen in cell M.sub.21 of Table 12, each of the
four indirect equation results agree with the direct equation value
given in cell M.sub.21 of Table 11. Hence, there is a very strong
probability that the conclusions given by both tables for cell
M.sub.12 is correct. Note that cell M.sub.12 is the negative of
cell M.sub.21 as previously shown in Equation 6. TABLE-US-00012
TABLE 12 Indirect Cycle Count Offset Matrix (Initial Data) M.sub.11
= 0 M.sub.12 = M.sub.13 - M.sub.13 = M.sub.12 - M.sub.14 = M.sub.12
- M.sub.15 = M.sub.12 - M.sub.16 = M.sub.12 - M.sub.23 = 2 M.sub.32
= -4 M.sub.42 = -7 M.sub.52 = -7 M.sub.62 = -247 M.sub.12 =
M.sub.14 - M.sub.13 = M.sub.14 - M.sub.14 = M.sub.13 - M.sub.15 =
M.sub.13 - M.sub.16 = M.sub.13 - M.sub.24 = 2 M.sub.34 = -4
M.sub.43 = -7 M.sub.53 = -7 M.sub.63 = -7 M.sub.12 = M.sub.15 -
M.sub.13 = M.sub.15 - M.sub.14 = M.sub.15 - M.sub.15 = M.sub.14 -
M.sub.16 = M.sub.14 - M.sub.25 = 2 M.sub.35 = -4 M.sub.45 = -7
M.sub.54 = -7 M.sub.64 = -7 M.sub.12 = M.sub.16 - M.sub.13 =
M.sub.16 - M.sub.14 = M.sub.16 - M.sub.15 = M.sub.16 - M.sub.16 =
M.sub.15 - M.sub.26 = 2 M.sub.36 = -244 M.sub.46 = -247 M.sub.56 =
-247 M.sub.65 = -7 M.sub.21 = M.sub.23 - M.sub.22 = 0 M.sub.23 =
M.sub.21 - M.sub.24 = M.sub.21 - M.sub.25 = M.sub.21 - M.sub.26 =
M.sub.21 - M.sub.13 = -2 M.sub.31 = -6 M.sub.41 = -9 M.sub.51 = -9
M.sub.61 = -249 M.sub.21 = M.sub.24 - M.sub.23 = M.sub.24 -
M.sub.24 = M.sub.23 - M.sub.25 = M.sub.23 - M.sub.26 = M.sub.23 -
M.sub.14 = -2 M.sub.34 = -6 M.sub.43 = -9 M.sub.53 = -9 M.sub.63 =
-9 M.sub.21 = M.sub.25 - M.sub.23 = M.sub.25 - M.sub.24 = M.sub.25
- M.sub.25 = M.sub.24 - M.sub.26 = M.sub.24 - M.sub.15 = -2
M.sub.35 = -6 M.sub.45 = -9 M.sub.54 = -9 M.sub.64 = -9 M.sub.21 =
M.sub.26 - M.sub.23 = M.sub.26 - M.sub.24 = M.sub.26 - M.sub.25 =
M.sub.26 - M.sub.26 = M.sub.25 - M.sub.16 = -2 M.sub.36 = -246
M.sub.46 = -249 M.sub.56 = -249 M.sub.65 = -9 M.sub.31 = M.sub.32 -
M.sub.32 = M.sub.31 - M.sub.33 = 0 M.sub.34 = M.sub.31 - M.sub.35 =
M.sub.31 - M.sub.36 = M.sub.31 - M.sub.12 = 4 M.sub.21 = 6 M.sub.41
= -3 M.sub.51 = -3 M.sub.61 = -243 M.sub.31 = M.sub.34 - M.sub.32 =
M.sub.34 - M.sub.34 = M.sub.32 - M.sub.35 = M.sub.32 - M.sub.36 =
M.sub.32 - M.sub.14 = 4 M.sub.24 = 6 M.sub.42 = -3 M.sub.52 = -3
M.sub.62 = -243 M.sub.31 = M.sub.35 - M.sub.32 = M.sub.35 -
M.sub.34 = M.sub.35 - M.sub.35 = M.sub.34 - M.sub.36 = M.sub.34 -
M.sub.15 = 4 M.sub.25 = 6 M.sub.45 = -3 M.sub.54 = -3 M.sub.64 = -3
M.sub.31 = M.sub.36 - M.sub.32 = M.sub.36 - M.sub.34 = M.sub.36 -
M.sub.35 = M.sub.36 - M.sub.36 = M.sub.35 - M.sub.16 = 244 M.sub.26
= 246 M.sub.46 = -3 M.sub.56 = -3 M.sub.65 = -3 M.sub.41 = M.sub.42
- M.sub.42 = M.sub.41 - M.sub.43 = M.sub.41 - M.sub.44 = 0 M.sub.45
= M.sub.41 - M.sub.46 = M.sub.41 - M.sub.12 = 7 M.sub.21 = 9
M.sub.31 = 3 M.sub.51 = 0 M.sub.61 = -240 M.sub.41 = M.sub.43 -
M.sub.42 = M.sub.43 - M.sub.43 = M.sub.42 - M.sub.45 = M.sub.42 -
M.sub.46 = M.sub.42 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32 = 3
M.sub.52 = 0 M.sub.62 = -240 M.sub.41 = M.sub.45 - M.sub.42 =
M.sub.45 - M.sub.43 = M.sub.45 - M.sub.45 = M.sub.43 - M.sub.46 =
M.sub.43 - M.sub.15 = 7 M.sub.25 = 9 M.sub.35 = 3 M.sub.53 = 0
M.sub.63 = 0 M.sub.41 = M.sub.46 - M.sub.42 = M.sub.46 - M.sub.43 =
M.sub.46 - M.sub.45 = M.sub.46 - M.sub.46 = M.sub.45 - M.sub.16 =
247 M.sub.26 = 249 M.sub.36 = 3 M.sub.56 = 0 M.sub.65 = 0 M.sub.51
= M.sub.52 - M.sub.52 = M.sub.51 - M.sub.53 = M.sub.51 - M.sub.54 =
M.sub.51 - M.sub.55 = 0 M.sub.56 = M.sub.51 - M.sub.12 = 7 M.sub.21
= 9 M.sub.31 = 3 M.sub.41 = 0 M.sub.61 = -240 M.sub.51 = M.sub.53 -
M.sub.52 = M.sub.53 - M.sub.53 = M.sub.52 - M.sub.54 = M.sub.52 -
M.sub.56 = M.sub.52 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32 = 3
M.sub.42 = 0 M.sub.62 = -240 M.sub.51 = M.sub.54 - M.sub.52 =
M.sub.54 - M.sub.53 = M.sub.54 - M.sub.54 = M.sub.53 - M.sub.56 =
M.sub.53 - M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3 M.sub.43 = 0
M.sub.63 = 0 M.sub.51 = M.sub.56 - M.sub.52 = M.sub.56 - M.sub.53 =
M.sub.56 - M.sub.54 = M.sub.56 - M.sub.56 = M.sub.54 - M.sub.16 =
247 M.sub.26 = 249 M.sub.36 = 3 M.sub.46 = 0 M.sub.64 = 0 M.sub.61
= M.sub.62 - M.sub.62 = M.sub.61 - M.sub.63 = M.sub.61 - M.sub.64 =
M.sub.61 - M.sub.65 = M.sub.61 - M.sub.66 = 0 M.sub.12 = 247
M.sub.21 = 249 M.sub.31 = 243 M.sub.41 = 240 M.sub.51 = 240
M.sub.61 = M.sub.63 - M.sub.62 = M.sub.83 - M.sub.63 = M.sub.62 -
M.sub.64 = M.sub.62 - M.sub.65 = M.sub.62 - M.sub.13 = 7 M.sub.23 =
9 M.sub.32 = 243 M.sub.42 = 240 M.sub.52 = 240 M.sub.61 = M.sub.64
- M.sub.62 = M.sub.64 - M.sub.63 = M.sub.64 - M.sub.64 = M.sub.63 -
M.sub.65 = M.sub.63 - M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3
M.sub.43 = 0 M.sub.53 = 0 M.sub.61 = M.sub.65 - M.sub.62 = M.sub.65
- M.sub.63 = M.sub.65 - M.sub.64 = M.sub.65 - M.sub.65 = M.sub.64 -
M.sub.15 = 7 M.sub.25 = 9 M.sub.35 = 3 M.sub.45 = 0 M.sub.54 =
0
[0174] Reviewing cell M.sub.31 in Tables 11 and 12 shows all but
one calculated result (M.sub.31=M.sub.36-M.sub.16=244) to be in
agreement (that M.sub.31=4). Thus, the statistical mode in this
sample is 4, with M.sub.36-M.sub.16 deviating greatly from the mode
(1408). Two things can be learned from this cell. First, because of
the near unanimity from the measured and calculated values, the
direct cycle count offset between device M.sub.3 and M.sub.1 is
almost certainly equal to 4 cycles. Second, the direct cycle count
offsets of either cell M.sub.36 and/or M.sub.16 are incorrect in
Table 11. The noisy data alignment algorithm 1400 notes these two
facts for future reference in the final analysis. No more
conclusions can be drawn from this cell alone.
[0175] Reviewing cell M.sub.41 in Tables 11 and 12 again shows all
but one calculated result (M.sub.41=M.sub.46-M.sub.16=247) to be in
agreement (that M.sub.41=7). Thus, the statistical mode for this
sample is 7 with M.sub.46-M.sub.16 deviating greatly from the mode
(1408). Three things can be learned from this cell based on the
discussion above in connection with cell M.sub.31. First, because
of the near unanimity from the measured and calculated values, the
direct cycle count offset between device D.sub.4 and D.sub.1 is
almost certainly equal to 7 cycles. Second, the direct cycle count
offsets of either cell M.sub.46 and/or M.sub.16 are incorrect in
Table 11. Third, based on the conclusions from cell M.sub.31 and
the conclusions in the previous sentence, cell M.sub.16 is now
beginning to look suspicious. Again, the noisy data alignment
algorithm 1400 notes these facts for future reference in the final
analysis. No more conclusions can be drawn from this cell
alone.
[0176] Reviewing cell M.sub.51 in Tables 11 and 12 again shows all
but one calculated result (M.sub.51=M.sub.56-M.sub.16=247) to be in
agreement (that M.sub.51=7). Thus, the statistical mode for this
sample is 7 with M.sub.56-M.sub.16 deviating greatly from the mode
(1408). Because of the near unanimity from the measured and
calculated values, the direct cycle count offset between device
M.sub.5 and M.sub.1 is almost certainly equal to 7 cycles. Again,
the direct cycle count offsets of either cell M.sub.56 and/or
M.sub.16 are incorrect in Table 11. Finally, based on the
conclusions from cells M.sub.31 and M.sub.41 above, cell M.sub.16
is now looking extremely suspicious. Once again, the noisy data
alignment algorithm 1400 notes these facts for future reference in
the final analysis.
[0177] Reviewing cell M.sub.61 in Tables 11 and 12 shows two of the
five relationships providing one answer
(M.sub.61=M.sub.62-M.sub.12=247) and remaining three providing
another answer (M.sub.61=7). Thus, the statistical mode for this
sample is also 7, with M.sub.62-M.sub.12 deviating greatly from the
mode (1408). Of the two relationships providing the answer
M.sub.61=247, one was the direct relationship (M.sub.6-M.sub.1)
(see cell M.sub.61 in Table 11). In the previous two paragraphs,
suspicion was cast upon the validity of the direct relationship for
M.sub.61 (and thus M.sub.16) because these offset values deviated
from the statistical mode. It now becomes apparent that
M.sub.61.noteq.247 (M.sub.16.noteq.-247). This conclusion is
further established after analyzing M.sub.62, M.sub.13, M.sub.63,
M.sub.14, M.sub.64, M.sub.15, M.sub.65, M.sub.26, M.sub.36,
M.sub.46, and M.sub.56 in Tables 11 and 12. In all cases, the
logical choice for the direct cycle count offsets of M.sub.61 and
M.sub.16 in Table 11 is (7) and (-7) respectively.
[0178] It may not always be the case that the data from the
indirect cycle count offset matrix will be useful as shown above.
For example, it may not be possible to determine a statistical mode
for a given set of indirect cycle count offsets because they may
all be unique values (indicating many noisy device relationships).
Alternately, there may be multiple statistical modes such as when
multiple indirect cycle count offsets appear in equal numbers. When
the data from the indirect cycle count offset matrix is
unproductive (1410), the algorithm 1400 may return control to the
data alignment algorithm 108 whereupon the monitoring devices are
instructed to send another batch of data indicative of frequency
variations for analysis by the data alignment algorithm.
TABLE-US-00013 TABLE 13 Direct Cycle Count Offset Matrix (Iteration
1) Device M.sub.1 M.sub.2 M.sub.3 M.sub.4 M.sub.5 M.sub.6 M.sub.1 0
2 -4 -7 -7 -7 M.sub.2 -2 0 -6 -9 -9 -249 M.sub.3 4 6 0 -3 -3 -3
M.sub.4 7 9 3 0 0 0 M.sub.5 7 9 3 0 0 0 M.sub.6 7 249 3 0 0 0
[0179] The noisy data alignment algorithm 1400 determines the data
cell in the direct cycle count offset matrix (Table 11) to adjust
and adjusts Table 11 by changing cell M.sub.61 to (7) and cell
M.sub.16 to (-7) (1412), resulting in Table 13. Furthermore,
changing any direct relationship value(s) necessitates revising the
indirect relationship results as well (1414). The noisy data
alignment algorithm 1400 builds Table 14 with the updated results
of each indirect relationship to reflect the changes made to the
direct relationship data (1414). TABLE-US-00014 TABLE 14 Indirect
Cycle Count Offset Matrix (Iteration 1) M.sub.11 = 0 M.sub.12 =
M.sub.13 - M.sub.13 = M.sub.12 - M.sub.14 = M.sub.12 - M.sub.15 =
M.sub.12 - M.sub.16 = M.sub.12 - M.sub.23 = 2 M.sub.32 = -4
M.sub.42 = -7 M.sub.52 = -7 M.sub.62 = -247 M.sub.12 = M.sub.14 -
M.sub.13 = M.sub.14 - M.sub.14 = M.sub.13 - M.sub.15 = M.sub.13 -
M.sub.16 = M.sub.13 - M.sub.24 = 2 M.sub.34 = -4 M.sub.43 = -7
M.sub.53 = -7 M.sub.63 = -7 M.sub.12 = M.sub.15 - M.sub.13 =
M.sub.15 - M.sub.14 = M.sub.15 - M.sub.15 = M.sub.14 - M.sub.16 =
M.sub.14 - M.sub.25 = 2 M.sub.35 = -4 M.sub.45 = -7 M.sub.54 = -7
M.sub.64 = -7 M.sub.12 = M.sub.16 - M.sub.13 = M.sub.16 - M.sub.14
= M.sub.16 - M.sub.15 = M.sub.16 - M.sub.16 = M.sub.15 - M.sub.26 =
242 M.sub.36 = -4 M.sub.46 = -7 M.sub.56 = -7 M.sub.65 = -7
M.sub.21 = M.sub.23 - M.sub.22 = 0 M.sub.23 = M.sub.21 - M.sub.24 =
M.sub.21 - M.sub.25 = M.sub.21 - M.sub.26 = M.sub.21 - M.sub.13 =
-2 M.sub.31 = -6 M.sub.41 = -9 M.sub.51 = -9 M.sub.61 = -9 M.sub.21
= M.sub.24 - M.sub.23 = M.sub.24 - M.sub.24 = M.sub.23 - M.sub.25 =
M.sub.23 - M.sub.26 = M.sub.23 - M.sub.14 = -2 M.sub.34 = -6
M.sub.43 = -9 M.sub.53 = -9 M.sub.63 = -9 M.sub.21 = M.sub.25 -
M.sub.23 = M.sub.25 - M.sub.24 = M.sub.25 - M.sub.25 = M.sub.24 -
M.sub.26 = M.sub.24 - M.sub.15 = -2 M.sub.35 = -6 M.sub.45 = -9
M.sub.54 = -9 M.sub.64 = -9 M.sub.21 = M.sub.26 - M.sub.23 =
M.sub.26 - M.sub.24 = M.sub.26 - M.sub.25 = M.sub.26 - M.sub.28 =
M.sub.25 - M.sub.16 = -242 M.sub.36 = -246 M.sub.46 = -249 M.sub.56
= -249 M.sub.65 = -9 M.sub.31 = M.sub.32 - M.sub.32 = M.sub.31 -
M.sub.33 = 0 M.sub.34 = M.sub.31 - M.sub.35 = M.sub.31 - M.sub.36 =
M.sub.31 - M.sub.12 = 4 M.sub.21 = 6 M.sub.41 = -3 M.sub.51 = -3
M.sub.61 = -3 M.sub.31 = M.sub.34 - M.sub.32 = M.sub.34 - M.sub.34
= M.sub.32 - M.sub.35 = M.sub.32 - M.sub.36 = M.sub.32 - M.sub.14 =
4 M.sub.24 = 6 M.sub.42 = -3 M.sub.52 = -3 M.sub.82 = -243 M.sub.31
= M.sub.35 - M.sub.32 = M.sub.35 - M.sub.34 = M.sub.35 - M.sub.35 =
M.sub.34 - M.sub.36 = M.sub.34 - M.sub.15 = 4 M.sub.25 = 6 M.sub.45
= -3 M.sub.54 = -3 M.sub.64 = -3 M.sub.31 = M.sub.36 - M.sub.32 =
M.sub.36 - M.sub.34 = M.sub.36 - M.sub.35 = M.sub.36 - M.sub.36 =
M.sub.35 - M.sub.16 = 4 M.sub.26 = 246 M.sub.46 = -3 M.sub.56 = -3
M.sub.65 = -3 M.sub.41 = M.sub.42 - M.sub.42 = M.sub.41 - M.sub.43
= M.sub.41 - M.sub.44 = 0 M.sub.45 = M.sub.41 - M.sub.46 = M.sub.41
- M.sub.12 = 7 M.sub.21 = 9 M.sub.31 = 3 M.sub.51 = 0 M.sub.61 = 0
M.sub.41 = M.sub.43 - M.sub.42 = M.sub.43 - M.sub.43 = M.sub.42 -
M.sub.45 = M.sub.42 - M.sub.46 = M.sub.42 - M.sub.13 = 7 M.sub.23 =
9 M.sub.32 = 3 M.sub.52 = 0 M.sub.62 = -240 M.sub.41 = M.sub.45 -
M.sub.42 = M.sub.45 - M.sub.43 = M.sub.45 - M.sub.45 = M.sub.43 -
M.sub.46 = M.sub.43 - M.sub.15 = 7 M.sub.25 = 9 M.sub.35 = 3
M.sub.53 = 0 M.sub.63 = 0 M.sub.41 = M.sub.46 - M.sub.42 = M.sub.46
- M.sub.43 = M.sub.46 - M.sub.45 = M.sub.46 - M.sub.46 = M.sub.45 -
M.sub.16 = 7 M.sub.26 = 249 M.sub.36 = 3 M.sub.56 = 0 M.sub.65 = 0
M.sub.51 = M.sub.52 - M.sub.52 = M.sub.51 - M.sub.53 = M.sub.51 -
M.sub.54 = M.sub.51 - M.sub.55 = 0 M.sub.56 = M.sub.51 - M.sub.12 =
7 M.sub.21 = 9 M.sub.31 = 3 M.sub.41 = 0 M.sub.61 = 0 M.sub.51 =
M.sub.53 - M.sub.52 = M.sub.53 - M.sub.53 = M.sub.52 - M.sub.54 =
M.sub.52 - M.sub.56 = M.sub.52 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32
= 3 M.sub.42 = 0 M.sub.62 = -240 M.sub.51 = M.sub.54 - M.sub.52 =
M.sub.54 - M.sub.53 = M.sub.54 - M.sub.54 = M.sub.53 - M.sub.56 =
M.sub.53 - M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3 M.sub.43 = 0
M.sub.63 = 0 M.sub.51 = M.sub.56 - M.sub.52 = M.sub.56 - M.sub.53 =
M.sub.56 - M.sub.54 = M.sub.56 - M.sub.56 = M.sub.54 - M.sub.16 = 7
M.sub.26 = 249 M.sub.36 = 3 M.sub.46 = 0 M.sub.64 = 0 M.sub.61 =
M.sub.62 - M.sub.62 = M.sub.61 - M.sub.63 = M.sub.61 - M.sub.64 =
M.sub.61 - M.sub.65 = M.sub.61 - M.sub.66 = 0 M.sub.12 = 247
M.sub.21 = 9 M.sub.31 = 3 M.sub.41 = 0 M.sub.51 = 0 M.sub.61 =
M.sub.63 - M.sub.62 = M.sub.63 - M.sub.63 = M.sub.62 - M.sub.64 =
M.sub.62 - M.sub.65 = M.sub.62 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32
= 243 M.sub.42 = 240 M.sub.52 = 240 M.sub.61 = M.sub.64 - M.sub.62
= M.sub.64 - M.sub.63 = M.sub.64 - M.sub.64 = M.sub.63 - M.sub.65 =
M.sub.63 - M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3 M.sub.43 = 0
M.sub.53 = 0 M.sub.61 = M.sub.65 - M.sub.62 = M.sub.65 - M.sub.63 =
M.sub.65 - M.sub.64 = M.sub.65 - M.sub.65 = M.sub.64 - M.sub.15 = 7
M.sub.25 = 9 M.sub.35 = 3 M.sub.45 = 0 M.sub.54 = 0
[0180] Reviewing cell M.sub.21 in Tables 13 and 14 shows all but
one calculated result (M.sub.21=M.sub.26-M.sub.16=-242) to be in
agreement (that M.sub.21=-2). This is curious because cell M.sub.21
from Table 12 showed agreement among all relationships (both direct
and indirect). However, because cells M.sub.61 and M.sub.16 were
later shown to be inaccurate, this can only mean that cells
M.sub.26 and M.sub.62 are incorrect as well. Further analyzing the
relationships in cells M.sub.61, M.sub.12, M.sub.32, M.sub.42,
M.sub.52, M.sub.23, M.sub.63, M.sub.24, M.sub.64, M.sub.25,
M.sub.65, M.sub.16, M.sub.36, M.sub.46, and M.sub.56 of Table 14
and cells M.sub.62 and M.sub.26 of Table 13 validate the conclusion
that the direct cycle count offsets in cells M.sub.26 and M.sub.62
of Table 13 are indeed incorrect. Cell M.sub.62 of Table 14
unanimously concludes that cell M.sub.62 of Table 13 should equal
(9). Cell M.sub.26 of Table 14 also unanimously concludes that cell
M.sub.26 of Table 13 should equal (-9). A significant advantage of
this noisy data alignment algorithm 1400 is that there can be only
one solution; there will be no ambiguity as to the correct offset
value to the modified in the direct cycle count offset matrix.
TABLE-US-00015 TABLE 15 Direct Cycle Count Offset Matrix (Iteration
2) Device M.sub.1 M.sub.2 M.sub.3 M.sub.4 M.sub.5 M.sub.6 M.sub.1 0
2 -4 -7 -7 -7 M.sub.2 -2 0 -6 -9 -9 -9 M.sub.3 4 6 0 -3 -3 -3
M.sub.4 7 9 3 0 0 0 M.sub.5 7 9 3 0 0 0 M.sub.6 7 9 3 0 0 0
[0181] The noisy data alignment algorithm adjusts Table 13 by
changing cell M.sub.62 to (9) and cell M.sub.26 to (-9) (1412) to
produce see Table 15. Again, changing any direct relationship
value(s) necessitates revising the indirect relationship results as
well (1414). The noisy data alignment algorithm 1440 builds Table
16 with the updated results of each indirect relationship to
reflect the changes made to the direct relationship data (1414).
Analysis of both Tables 15 and 16 reveals that all direct and
indirect relationships are in consensus and the results given in
these tables are the solution (1416). TABLE-US-00016 TABLE 16
Indirect Cycle Count Offset Matrix (Iteration 2) M.sub.11 = 0
M.sub.12 = M.sub.13 - M.sub.13 = M.sub.12 - M.sub.14 = M.sub.12 -
M.sub.15 = M.sub.12 - M.sub.16 = M.sub.12 - M.sub.23 = 2 M.sub.32 =
-4 M.sub.42 = -7 M.sub.52 = -7 M.sub.62 = -7 M.sub.12 = M.sub.14 -
M.sub.13 = M.sub.14 - M.sub.14 = M.sub.13 - M.sub.15 = M.sub.13 -
M.sub.16 = M.sub.13 - M.sub.24 = 2 M.sub.34 = -4 M.sub.43 = -7
M.sub.53 = -7 M.sub.63 = -7 M.sub.12 = M.sub.15 - M.sub.13 =
M.sub.15 - M.sub.14 = M.sub.15 - M.sub.15 = M.sub.14 - M.sub.16 =
M.sub.14 - M.sub.25 = 2 M.sub.35 = -4 M.sub.45 = -7 M.sub.54 = -7
M.sub.64 = -7 M.sub.12 = M.sub.16 - M.sub.13 = M.sub.16 - M.sub.14
= M.sub.16 - M.sub.15 = M.sub.16 - M.sub.16 = M.sub.15 - M.sub.26 =
2 M.sub.36 = -4 M.sub.46 = -7 M.sub.56 = -7 M.sub.65 = -7 M.sub.21
= M.sub.23 - M.sub.22 = 0 M.sub.23 = M.sub.21 - M.sub.24 = M.sub.21
- M.sub.25 = M.sub.21 - M.sub.26 = M.sub.21 - M.sub.13 = -2
M.sub.31 = -6 M.sub.41 = -9 M.sub.51 = -9 M.sub.61 = -9 M.sub.21 =
M.sub.24 - M.sub.23 = M.sub.24 - M.sub.24 = M.sub.23 - M.sub.25 =
M.sub.23 - M.sub.26 = M.sub.23 - M.sub.14 = -2 M.sub.34 = -6
M.sub.43 = -9 M.sub.53 = -9 M.sub.63 = -9 M.sub.21 = M.sub.25 -
M.sub.23 = M.sub.25 - M.sub.24 = M.sub.25 - M.sub.25 = M.sub.24 -
M.sub.26 = M.sub.24 - M.sub.15 = -2 M.sub.35 = -6 M.sub.45 = -9
M.sub.54 = -9 M.sub.64 = -9 M.sub.21 = M.sub.26 - M.sub.23 =
M.sub.26 - M.sub.24 = M.sub.26 - M.sub.25 = M.sub.26 - M.sub.26 =
M.sub.25 - M.sub.16 = -2 M.sub.36 = -6 M.sub.46 = -9 M.sub.56 = -9
M.sub.65 = -9 M.sub.31 = M.sub.32 - M.sub.32 = M.sub.31 - M.sub.33
= 0 M.sub.34 = M.sub.31 - M.sub.35 = M.sub.31 - M.sub.36 = M.sub.31
- M.sub.12 = 4 M.sub.21 = 6 M.sub.41 = -3 M.sub.51 = -3 M.sub.61 =
-3 M.sub.31 = M.sub.34 - M.sub.32 = M.sub.34 - M.sub.34 = M.sub.32
- M.sub.35 = M.sub.32 - M.sub.36 = M.sub.32 - M.sub.14 = 4 M.sub.24
= 6 M.sub.42 = -3 M.sub.52 = -3 M.sub.62 = -3 M.sub.31 = M.sub.35 -
M.sub.32 = M.sub.35 - M.sub.34 = M.sub.35 - M.sub.35 = M.sub.34 -
M.sub.36 = M.sub.34 - M.sub.15 = 4 M.sub.25 = 6 M.sub.45 = -3
M.sub.54 = -3 M.sub.64 = -3 M.sub.31 = M.sub.36 - M.sub.32 =
M.sub.36 - M.sub.34 = M.sub.36 - M.sub.35 = M.sub.36 - M.sub.36 =
M.sub.35 - M.sub.16 = 4 M.sub.26 = 6 M.sub.46 = -3 M.sub.56 = -3
M.sub.65 = -3 M.sub.41 = M.sub.42 - M.sub.42 = M.sub.41 - M.sub.43
= M.sub.41 - M.sub.44 = 0 M.sub.45 = M.sub.41 - M.sub.46 = M.sub.41
- M.sub.12 = 7 M.sub.21 = 9 M.sub.31 = 3 M.sub.51 = 0 M.sub.61 = 0
M.sub.41 = M.sub.43 - M.sub.42 = M.sub.43 - M.sub.43 = M.sub.42 -
M.sub.45 = M.sub.42 - M.sub.46 = M.sub.42 - M.sub.13 = 7 M.sub.23 =
9 M.sub.32 = 3 M.sub.52 = 0 M.sub.62 = 0 M.sub.41 = M.sub.45 -
M.sub.42 = M.sub.45 - M.sub.43 = M.sub.45 - M.sub.45 = M.sub.43 -
M.sub.46 = M.sub.43 - M.sub.15 = 7 M.sub.25 = 9 M.sub.35 = 3
M.sub.53 = 0 M.sub.63 = 0 M.sub.41 = M.sub.46 - M.sub.42 = M.sub.46
- M.sub.43 = M.sub.46 - M.sub.45 = M.sub.46 - M.sub.46 = M.sub.45 -
M.sub.16 = 7 M.sub.26 = 9 M.sub.36 = 3 M.sub.56 = 0 M.sub.65 = 0
M.sub.51 = M.sub.52 - M.sub.52 = M.sub.51 - M.sub.53 = M.sub.51 -
M.sub.54 = M.sub.51 - M.sub.55 = 0 M.sub.56 = M.sub.51 - M.sub.12 =
7 M.sub.21 = 9 M.sub.31 = 3 M.sub.41 = 0 M.sub.61 = 0 M.sub.51 =
M.sub.53 - M.sub.52 = M.sub.53 - M.sub.53 = M.sub.52 - M.sub.54 =
M.sub.52 - M.sub.56 = M.sub.52 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32
= 3 M.sub.42 = 0 M.sub.62 = 0 M.sub.51 = M.sub.54 - M.sub.52 =
M.sub.54 - M.sub.53 = M.sub.54 - M.sub.54 = M.sub.53 - M.sub.56 =
M.sub.53 - M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3 M.sub.43 = 0
M.sub.63 = 0 M.sub.51 = M.sub.56 - M.sub.52 = M.sub.56 - M.sub.53 =
M.sub.56 - M.sub.54 = M.sub.56 - M.sub.56 = M.sub.54 - M.sub.16 = 7
M.sub.26 = 9 M.sub.36 = 3 M.sub.46 = 0 M.sub.64 = 0 M.sub.61 =
M.sub.62 - M.sub.62 = M.sub.61 - M.sub.63 = M.sub.61 - M.sub.64 =
M.sub.61 - M.sub.65 = M.sub.61 - M.sub.66 = 0 M.sub.12 = 7 M.sub.21
= 9 M.sub.31 = 3 M.sub.41 = 0 M.sub.51 = 0 M.sub.61 = M.sub.63 -
M.sub.62 = M.sub.63 - M.sub.63 = M.sub.62 - M.sub.64 = M.sub.62 -
M.sub.65 = M.sub.62 - M.sub.13 = 7 M.sub.23 = 9 M.sub.32 = 3
M.sub.42 = 0 M.sub.52 = 0 M.sub.61 = M.sub.64 - M.sub.62 = M.sub.64
- M.sub.63 = M.sub.64 - M.sub.64 = M.sub.63 - M.sub.65 = M.sub.63 -
M.sub.14 = 7 M.sub.24 = 9 M.sub.34 = 3 M.sub.43 = 0 M.sub.53 = 0
M.sub.61 = M.sub.65 - M.sub.62 = M.sub.65 - M.sub.63 = M.sub.65 -
M.sub.64 = M.sub.65 - M.sub.65 = M.sub.64 - M.sub.15 = 7 M.sub.25 =
9 M.sub.35 = 3 M.sub.45 = 0 M.sub.54 = 0
Examination of Results
[0182] There were a total of 15 unique relationships as shown in
Table 10. It was necessary to adjust two of these direct
relationships to determine the actual solution and bring accord to
intertwined cycle count offset relationships between all devices.
Device D.sub.6 apparently had a noisy relationship with both
devices D.sub.1 and D.sub.2 as revealed in the analysis above.
Fortunately, device D.sub.6 did not have a noisy relationship with
all devices, and the noisy data alignment algorithm used that fact
to its advantage.
[0183] Once the solution in Table 15 has been determined by the
noisy data alignment algorithm 1400, the cycle counts in all of the
monitoring devices may be either adjusted to the same cycle count
based upon the solutions reported in Table 15 (1418) or the cycle
count offsets for each device pair may be stored and tracked by the
data alignment system 104 to be used accordingly. For example, when
a steady-state phenomenon or non steady-state phenomenon (also
referred to generally as an event) (as those terms are defined in
the IEEE and IEC standards) occurs on the power system being
monitored, the data alignment system 104 accesses the direct cycle
count offset matrix, as modified by the noisy data alignment
algorithm 1400, to determine whether the monitoring devices
perceived the same event or steady-state phenomenon or different
ones. To do so, the cycle count offsets of each capable device
reporting the event of steady-state phenomenon are accounted for by
referencing the direct cycle count offset table, which may include
modified offset values as determined by the noisy data alignment
algorithm 1400. For example, without alignment, D.sub.6 and D.sub.1
appear to report different events occurring at different cycles
that are 247 counts apart. But after adjustment by the noisy data
alignment algorithm 1400, the data alignment system 104 learns that
these devices are actually only 7 cycle counts apart and further
that they are both monitoring the same event or phenomenon. This
alignment of data is an invaluable tool for further analysis,
reporting, and alarming based upon the signal data received from
the monitoring devices.
[0184] The software application 110 may communicate instructions to
each of the monitoring devices whose cycle counters need to be
adjusted, signals indicative of a number of cycle counts by which
the monitoring device must adjust its cycle counter. Alternately,
the software application 110 may instruct the monitoring devices to
reset their cycle counters in an order consistent with Table 15.
For example monitoring device D.sub.2 will be instructed to adjust
its cycle counter by 2 counts relative to monitoring device
D.sub.1.
[0185] As is shown in the example above, signal data representing
frequency variations from the monitoring devices was collected only
one time from which the solution (Table 15) was achieved without
superfluous influence of statistical probabilities. The solution
can be confirmed to be empirically correct with the use of a GPS
time system. The data alignment algorithm 180 is invoked sparingly,
thus reducing the bandwidth on the monitoring devices, the software
110, and communications network. Because data does not have to be
repeatedly collected from the devices, the overall speed and
efficiency of the automated data alignment process is substantially
increased. Finally and most importantly, a unique and compelling
technique is offered for noisy device pairs providing the data
alignment algorithm with enhanced robustness for the most difficult
systems.
[0186] It should be noted that there may be monitoring systems that
exhibit an extensive number of noisy device pair relationships, or
there may specific devices that demonstrate noisy relationships
with all other devices. This noisy data alignment solution has the
added benefit of being able to measure the validity and usefulness
of the data sample taken by the data alignment algorithm 180. A
single pass of the sample data through the noisy data alignment
algorithm 1400 is adequate to determine whether the data sample
will be useful based on the level of accord between the devices. In
the instances where the data sample is not useful, it may be
necessary to reinitialize and run the data alignment algorithm 180
to obtain a useful data sample that will iterate to the
solution.
[0187] The unexpected interconnection of relationships between the
cycle counts of monitoring devices on a power monitoring system as
described herein provided a way of solving a real-world dilemma.
The noisy data alignment solution represents a vital component in
reducing the overall cost of power monitoring systems while
improving the data analyses and solutions for the end-user.
Optional Verification of Results
[0188] As an optional verification of alignment based on the
cross-correlation of frequency between device pairs, it may be
helpful to evaluate alternative solutions given by the data
alignment algorithm 180. In the majority of cases, the cycle count
offset corresponding to the highest correlation is the correct
solution. However, as shown above, it is possible for the highest
correlation coefficient to be incorrect (as is the case for any
noisy device pair).
[0189] Data has shown that even when the incorrect solution is
given by the data alignment algorithm, the correct solution is
still determined to be a leading candidate among the most probable
correlations. For example, FIG. 13 illustrates exemplary
cross-correlation data from an exemplary device pair. FIG. 13 notes
the top five potential solutions given by the data alignment
algorithm corresponding to the top five highest correlation
coefficients 1302, 1304, 1306, 1308, 1310 of that device pair. Even
if the highest cross-correlation coefficient 1302 is incorrect,
data has shown the correct solution may still be one of the highest
cross-correlation coefficients (such as one of these five).
[0190] The optional verification algorithm 1420 enables a
comparison of the results given by the noisy data alignment
algorithm 1400 with multiple potential solutions given by the
cross-correlation data developed in the data alignment algorithm
180. FIG. 14B illustrates the optional verification algorithm
1420.
[0191] The verification algorithm 1420 develops a list of the most
probable cycle count offsets for a given device pair to be verified
(1422). Each correlation coefficient produced during the
cross-correlation is associated with a cycle count for each device.
Responsive to a default or user configuration, the number of cycle
count offsets 1424 to consider in the verification algorithm 1420
is accessed by the algorithm 1420. For example, one configuration
may test the top five correlation coefficients to determine whether
the adjusted cycle count offset corresponds to one of the top five
correlation coefficients. The results from the noisy data alignment
algorithm 1400 (such as Table 15) 1428 are accessed by the
algorithm 1420. The algorithm 1420 compares the offset values
determined by the noisy data alignment algorithm 1400 (e.g., the
values in the direct cycle count offset matrix Table 15) with the
list of the most probable cycle offsets (also referred to as
verification cycle count offsets) for the same given device pair
(1426). For example, for the offset M.sub.61=7, the verification
algorithm 1420 compares that offset with the offset calculated from
the cycle counts corresponding to the five highest correlation
coefficients 1302, 1304, 1306, 1308, 1310. If the cycle count
offset M.sub.61 matches any cycle count offsets calculated based
upon any of the five highest correlation coefficients 1302, 1304,
1306, 1308, 1310 (1430), then the algorithm 1420 reports a high
degree of confidence in the solution (1434). When the confidence in
the adjusted indirect cycle count offset is high (1434), the
algorithm 1420 determines whether all unique device pairs to be
verified have been verified (1438) or at least those device pairs
whose cycle count offsets were adjusted by the noisy data alignment
algorithm 1400, and if not, repeats the verification for the next
device pair until there are no further device pairs to be verified.
Otherwise, when the adjusted cycle count offset does not correspond
to any of the cycle count offsets calculated from the list of
probable cycle count offsets, the algorithm 1420 assigns the
confidence in the solution as low (1432), and, depending upon a
default or user configuration, the indirect relationship determined
by the algorithm 1420 may be accepted or the data alignment
algorithm 180 may be reinitiated to generate new data (1436). If
the default or user configuration requires reinitializing the data
alignment algorithm 180 to generate a new direct cycle count offset
matrix (1440), control of the algorithm 1420 is passed back to the
data alignment algorithm 180 (FIG. 5A).
[0192] While particular embodiments and applications of the present
invention have been illustrated and described, it is to be
understood that the invention is not limited to the precise
construction and compositions disclosed herein and that various
modifications, changes, and variations can be apparent from the
foregoing descriptions without departing from the spirit and scope
of the invention as defined in the appended claims.
* * * * *